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All questions of Trigonometry for Year 10 Exam
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If tan A = 3/2, then the value of cos A is- a)
- b)
- c)2/3
- d)
Correct answer is option 'B'. Can you explain this answer?
If tan A = 3/2, then the value of cos A is
a)
b)
c)
2/3
d)
|
Arun Sharma answered |
Tanθ = Perpendicular / Base
We are given that TanA = 3/2
On comparing
Perpendicular = 3
Base = 2
To fing hypotenuse
Hypotenuse2 = Perpendicular2 + Base2
Hypotenuse2 = 32 + 22
Hypotenuse =
Hypotenuse = 3.6
We are given that TanA = 3/2
On comparing
Perpendicular = 3
Base = 2
To fing hypotenuse
Hypotenuse2 = Perpendicular2 + Base2
Hypotenuse2 = 32 + 22
Hypotenuse =
Hypotenuse = 3.6
Cosθ = Base / Hypotenuse
CosA = 2 / 3.6
Hence the value of Cos A is 2/3.6=2/√13
CosA = 2 / 3.6
Hence the value of Cos A is 2/3.6=2/√13
If tan 
, then 
is equal to- a)24
- b)12/13
- c)25
- d)9
Correct answer is option 'C'. Can you explain this answer?
If tan , then is equal to
, then is equal toa)
24
b)
12/13
c)
25
d)
9
|
Raghav Bansal answered |
tanθ = 12/5
so sinθ = 12/13
so
(1 + 12/13)/(1-12/13)
= 25/1 = 25
Using the formula 
the value of sin 15° is- a)1
- b)0
- c)3
- d)
Correct answer is option 'D'. Can you explain this answer?
Using the formula the value of sin 15° is
the value of sin 15° isa)
1
b)
0
c)
3
d)
|
Diya Bansal answered |
Let θ= 15
so
cos 2(15)=1-2sin15^2
√(
cos30-1)/2)=-sin15√(
√3/2-1)/2)=-sin15
√(
√3-2)/4)=-sin15
√(2-
√3)/2=sin 15
Given that sin θ = a/b, then cos θ is equal to- a)
- b)b/a
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
Given that sin θ = a/b, then cos θ is equal to
a)
b)
b/a
c)
d)
|
|
Drishti Kumari answered |
Sin € = a / b = perpendicular / hypotenuse
Base = root under h^2 - p^2
Base = root under b^2 - a^2
cos € = base / hypotenuse
cos € = root under b^2 - a^2 / b
Hence option (C) is correct .
Base = root under h^2 - p^2
Base = root under b^2 - a^2
cos € = base / hypotenuse
cos € = root under b^2 - a^2 / b
Hence option (C) is correct .
The value of (sin 45° + cos 45°) is- a)1/√2
- b)√2
- c)√3/2
- d)1
Correct answer is option 'B'. Can you explain this answer?
The value of (sin 45° + cos 45°) is
a)
1/√2
b)
√2
c)
√3/2
d)
1
|
Krishna Iyer answered |
sin 45° + cos 45°
Hence, the answer is = √2
Hence, the answer is = √2
When 0°< θ < 90°, and 2cos θ = 1 the value of θ is
- a)30°
- b)50°
- c)60°
- d)40°
Correct answer is option 'C'. Can you explain this answer?
When 0°< θ < 90°, and 2cos θ = 1 the value of θ is
a)
30°
b)
50°
c)
60°
d)
40°
|
|
Ananya Das answered |
2cos θ = 1
cos θ = 1/2
θ = 60°
cos θ = 1/2
θ = 60°
The value of (sin 30° + cos 30°) - (sin 60° + cos 60°) is- a)-1
- b)0
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
The value of (sin 30° + cos 30°) - (sin 60° + cos 60°) is
a)
-1
b)
0
c)
1
d)
2
|
|
Ritu Saxena answered |
sin 30° = 1/2,
cos 30°=√3/2,
sin 60°=√3/2,
cos 60°=1/2,
By putting the value of sin 30°, cos 30°, sin 60° and cos 60° in equation
cos 30°=√3/2,
sin 60°=√3/2,
cos 60°=1/2,
By putting the value of sin 30°, cos 30°, sin 60° and cos 60° in equation
We get=
(sin30°+cos30°)-(sin60°+cos60°)=(1/2+√3/2)-(√3/2+1/2)
=0
(sin30°+cos30°)-(sin60°+cos60°)=(1/2+√3/2)-(√3/2+1/2)
=0
Can you explain the answer of this question below:If 7sin2x + 3cos2x = 4 then , secx + cosecx =- A:
- B:
- C:
- D:
The answer is a.
If 7sin2x + 3cos2x = 4 then , secx + cosecx =
A:
B:
C:
D:
|
|
Amit Kumar answered |
7sin2x+3cos2 x=4
7sin2x+3(1-sin2x)=4
7sin2x+3-3sin2x=4
4sin2x=4-3
4sin2x=1
sin2x=¼
sinx=½
Cosec x=1/sinx=2
Cos x=
Sec x= 1/cos x=
Cosec x + sec x=2+
7sin2x+3(1-sin2x)=4
7sin2x+3-3sin2x=4
4sin2x=4-3
4sin2x=1
sin2x=¼
sinx=½
Cosec x=1/sinx=2
Cos x=
Sec x= 1/cos x=
Cosec x + sec x=2+
tan A =- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
tan A =
a)
b)
c)
d)
|
|
Aashu Mehra answered |
ACTUALLY OPTION C IS ALSO NOT A PERFECT ANS BECAUSE when we solve it...it comes out sinA/mode cosA which means +tanA and -tanA
If tan θ = a/b then the value of 
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
If tan θ = a/b then the value of
a)
b)
c)
d)
|
|
Ananya Das answered |
Let,angle= θ
(asinθ + bcosθ)/(asinθ - bcosθ)
Dividing both numerator and denominator from cosθ
We get,
atanθ +b/atanθ - b
= ( a.a/b + b) /(a.a/b - b) =(a²/b +b)/(a²/b - b)
=(a² + b²/a²- b²)
(asinθ + bcosθ)/(asinθ - bcosθ)
Dividing both numerator and denominator from cosθ
We get,
atanθ +b/atanθ - b
= ( a.a/b + b) /(a.a/b - b) =(a²/b +b)/(a²/b - b)
=(a² + b²/a²- b²)
The value of the expression 
is- a)√3/2
- b)1/2
- c)1
- d)2
Correct answer is option 'C'. Can you explain this answer?
The value of the expression is
isa)
√3/2
b)
1/2
c)
1
d)
2
|
|
Krishna Iyer answered |
We know that sin 60 =√3/2 and cos 30 = √3/2.
Therefore , Sin 60/cos 30= (√3/2)/(√3/2) = 1
Therefore , Sin 60/cos 30= (√3/2)/(√3/2) = 1
The value of 
- a) 1/√2
- b) 1/√3
- c)√3
- d)1
Correct answer is option 'D'. Can you explain this answer?
The value of
a)
1/√2
b)
1/√3
c)
√3
d)
1
|
|
Amit Sharma answered |
we know
tan 30= 1/√3
cot60= 1/√3
cot60= 1/√3
tan30/cot60= 1/√3 ×√3/1= 1
The value of tan1°.tan2°.tan3°………. tan89° is :- a)2
- b)1
- c)1/2
- d)0
Correct answer is option 'B'. Can you explain this answer?
The value of tan1°.tan2°.tan3°………. tan89° is :
a)
2
b)
1
c)
1/2
d)
0
|
Meera Rana answered |
tan 1.tan 2.tan 3...tan (90 - 3 ).tan ( 90 - 2 ).tan ( 90 - 1)
=tan 1.tan 2 .tan 3...cot 3.cot 2.cot 1
=tan 1.cot 1.tan 2.cot 2.tan 3.cot 3 ... tan 89.cot 89
1 x 1 x 1 x 1 x ... x 1 =1
=tan 1.tan 2 .tan 3...cot 3.cot 2.cot 1
=tan 1.cot 1.tan 2.cot 2.tan 3.cot 3 ... tan 89.cot 89
1 x 1 x 1 x 1 x ... x 1 =1
The value of (tanl° tan2° tan3°... tan89°) is- a)0
- b)1
- c)2
- d)1/2
Correct answer is option 'B'. Can you explain this answer?
The value of (tanl° tan2° tan3°... tan89°) is
a)
0
b)
1
c)
2
d)
1/2
|
|
Krishna Iyer answered |
tan 1 . tan 2 . tan 3 ... tan 87 . tan 88 . tan 89 = LHS
tan 1 . tan 2 . tan 3 ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1)
tan 1 . tan 2 . tan 3 ... cot 3 . cot 2 . cot 1
tan 1 . tan 2 . tan 3 ... tan (90 - 3 ) . tan ( 90 - 2 ) . tan ( 90 - 1)
tan 1 . tan 2 . tan 3 ... cot 3 . cot 2 . cot 1
tan 1 . cot 1 . tan 2 . cot 2 . tan 3 . cot 3 ... tan 89 . cot 89
1 x 1 x 1 x 1 x ... x 1
As 1ⁿ = 1 = RHS
1 x 1 x 1 x 1 x ... x 1
As 1ⁿ = 1 = RHS
If ΔABC is right angled at C, then the value of cos (A + B) is- a)0
- b)1
- c)1/2
- d)√3/2
Correct answer is option 'A'. Can you explain this answer?
If ΔABC is right angled at C, then the value of cos (A + B) is
a)
0
b)
1
c)
1/2
d)
√3/2
|
Aniket Chavan answered |
Since ABC is right-angled and angle C is 90degree
therefore,
A+B=180degree - C
A+B=180degree-90degree
A+B= 90degree
Therefore,cos (A+B)=cos90degree
=0
The value of tan 1∘ tan 2∘ tan 3∘………… tan 89∘ is- a)0
- b)1
- c)12
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The value of tan 1∘ tan 2∘ tan 3∘………… tan 89∘ is
a)
0
b)
1
c)
12
d)
none of these
|
|
Krishna Iyer answered |
tan 1° tan2° tan3° ..............tan 89°
= tan(90° - 89°) tan(90° - 88°) tan(90° - 87°) ......... tan 87° tan 88° tan 89°
= cot 89° cot 88° cot 87° .............tan 87° tan 88° tan 89°
= (cot 89° tan 89°) (cot 88° tan 88°) (cot 87° tan 87°) .............(cot 44° tan 44°) tan 45°
= 1x1x1x1x1.........1 = 1
= tan(90° - 89°) tan(90° - 88°) tan(90° - 87°) ......... tan 87° tan 88° tan 89°
= cot 89° cot 88° cot 87° .............tan 87° tan 88° tan 89°
= (cot 89° tan 89°) (cot 88° tan 88°) (cot 87° tan 87°) .............(cot 44° tan 44°) tan 45°
= 1x1x1x1x1.........1 = 1
If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =- a)cot2B
- b)sec2B
- c)cos2B
- d)tan2B
Correct answer is option 'B'. Can you explain this answer?
If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A =
a)
cot2B
b)
sec2B
c)
cos2B
d)
tan2B
|
Siddharth answered |
ABC is a Δ, right angle at c.
1 +cot^2 =?........
we know that.....
Cosec^2 - cot^2= 1...
So,
=> 1+ cot^2
=> cosec^2 A
=> (AB)^2/( CB)^2
= sec ^2B.
The value of cos θ cos(90° - θ) – sin θ sin (90° - θ) is:
- a)1
- b)0
- c)-1
- d)2
Correct answer is option 'B'. Can you explain this answer?
The value of cos θ cos(90° - θ) – sin θ sin (90° - θ) is:
a)
1
b)
0
c)
-1
d)
2
|
Vikas Kumar answered |
Explanation:
- Given expression: cos θ cos(90° - θ) – sin θ sin (90° - θ)
- We know that cos(90° - θ) = sin θ and sin(90° - θ) = cos θ
- Substitute these values into the expression:
= cos θ * sin θ - sin θ * cos θ
= sin θ cos θ - sin θ cos θ
= 0
- Therefore, the value of the expression is 0.
- Given expression: cos θ cos(90° - θ) – sin θ sin (90° - θ)
- We know that cos(90° - θ) = sin θ and sin(90° - θ) = cos θ
- Substitute these values into the expression:
= cos θ * sin θ - sin θ * cos θ
= sin θ cos θ - sin θ cos θ
= 0
- Therefore, the value of the expression is 0.
sec θ is equal to –- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
sec θ is equal to –
a)
b)
c)
d)
|
|
Aman Rathore answered |
B is the correct answer
The value of cos2 17° – sin2 73° is- a)0
- b)1
- c)-1
- d)3
Correct answer is 'A'. Can you explain this answer?
The value of cos2 17° – sin2 73° is
a)
0
b)
1
c)
-1
d)
3
|
|
Amit Sharma answered |
cos217-sin273
=cos217-sin2(90-17)
=cos217-cos217 (because sin(90-x)=cos x)
=0
=cos217-sin2(90-17)
=cos217-cos217 (because sin(90-x)=cos x)
=0
If cosec A - cot A = 4/5, then cosec A = - a)47/40
- b)59/40
- c)51/40
- d)41/40
Correct answer is option 'D'. Can you explain this answer?
If cosec A - cot A = 4/5, then cosec A =
a)
47/40
b)
59/40
c)
51/40
d)
41/40
|
Abhiram Malik answered |
cosecA = 41/40
Explanation :
cosecA - cotA = 4/5 ---( 1 )
=> (cosecA - cotA)(cosecA + cotA)=(4/5) (cosecA + cotA)
=> (cosec�A-cot�A) = (4/5)(cosecA +cotA)
=> 1 = (4/5)(cosecA + cotA)
=> cosecA +cotA = 5/4 ---(2)
Now ,
Add (1) and (2 ), we get
=> 2coseecA = (4/5+5/4)
=> 2cosecA = (16+25)/20
=> cosecA = 41/40
Therefore,
cosecA = 41/40
9 sec2 A - 9tan2 A is equal to- a)1
- b)9
- c)8
- d)0
Correct answer is option 'B'. Can you explain this answer?
9 sec2 A - 9tan2 A is equal to
a)
1
b)
9
c)
8
d)
0
|
|
Kiran Mehta answered |
9 sec2 A - 9 tan2 A
= 9( sec2 A - tan2 A)
= 9 × 1
= 9
= 9( sec2 A - tan2 A)
= 9 × 1
= 9
If the length of a shadow cast by a pole is √3 times the length of the pole, then the angle of elevation of the sun is- a)45°
- b)60°
- c)30°
- d)90°
Correct answer is option 'C'. Can you explain this answer?
If the length of a shadow cast by a pole is √3 times the length of the pole, then the angle of elevation of the sun is
a)
45°
b)
60°
c)
30°
d)
90°
|
|
Anjana Khatri answered |
Consider the height of tower be h
∴ height of shadow =√3h .
In a triangle ABC,
tan ∠ACB = h / √3h
tan ∠ACB = 1 / √3
∠ACB = 30degree.
Therefore, angle of elevation is 30degree .
5 cot2 A – 5 cosec2 A =- a)– 5
- b)1
- c)0
- d)5
Correct answer is option 'A'. Can you explain this answer?
5 cot2 A – 5 cosec2 A =
a)
– 5
b)
1
c)
0
d)
5
|
Kalyan Jain answered |
Given: 5cot²A × 5cosec²A
To find: the value of the expression
Solution:
We know that:
cot²A = 1/(tan²A) and cosec²A = 1/(sin²A)
Substituting these values in the given expression, we get:
5cot²A × 5cosec²A = 5(1/(tan²A)) × 5(1/(sin²A))
= 25/(tan²A × sin²A)
But we know that:
tan²A × sin²A = (sinA/cosA)² × sin²A = sin³A/cos²A
Substituting this value in the expression, we get:
25/(tan²A × sin²A) = 25/(sin³A/cos²A)
= 25(cos²A/sin³A)
= 25cot²A × cosec²A
Substituting the values of cot²A and cosec²A, we get:
25cot²A × cosec²A = 25(1/(tan²A)) × 5(1/(sin²A))
= 25/(tan²A × sin²A)
We can see that this is the same expression that we started with.
Therefore, 5cot²A × 5cosec²A = 25/(tan²A × sin²A)
Answer: Option A) 5
To find: the value of the expression
Solution:
We know that:
cot²A = 1/(tan²A) and cosec²A = 1/(sin²A)
Substituting these values in the given expression, we get:
5cot²A × 5cosec²A = 5(1/(tan²A)) × 5(1/(sin²A))
= 25/(tan²A × sin²A)
But we know that:
tan²A × sin²A = (sinA/cosA)² × sin²A = sin³A/cos²A
Substituting this value in the expression, we get:
25/(tan²A × sin²A) = 25/(sin³A/cos²A)
= 25(cos²A/sin³A)
= 25cot²A × cosec²A
Substituting the values of cot²A and cosec²A, we get:
25cot²A × cosec²A = 25(1/(tan²A)) × 5(1/(sin²A))
= 25/(tan²A × sin²A)
We can see that this is the same expression that we started with.
Therefore, 5cot²A × 5cosec²A = 25/(tan²A × sin²A)
Answer: Option A) 5
Match the Columns:
- a)1 - A, 2 - C, 3 - B
- b)1 - B, 2 - C, 3 - A
- c)1 - B, 2 - C, 3 - D
- d)1 - D , 2 - B , 3 - A
Correct answer is option 'B'. Can you explain this answer?
Match the Columns:
a)
1 - A, 2 - C, 3 - B
b)
1 - B, 2 - C, 3 - A
c)
1 - B, 2 - C, 3 - D
d)
1 - D , 2 - B , 3 - A
|
|
Krishna Iyer answered |
Correct Answer :- b
Explanation : If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side.
If cos (40° + A) = sin 30°, the value of A is:
- a)60°
- b)20°
- c)40°
- d)30°
Correct answer is option 'B'. Can you explain this answer?
If cos (40° + A) = sin 30°, the value of A is:
a)
60°
b)
20°
c)
40°
d)
30°
|
|
Genius answered |
If you manage to memorise the trigonometry ratio table then you can easily tackle such problems in second. Here we can directly consider which cos value of θ is equals to Sin 30. So, if you have remembered that sin 30 = cos 60. so, 40+A=60, A= 20. This will help you to save much time in xam hall.
Out of the following options, the two angles that are together classified as complementary angles are- a)120° and 60°
- b)50° and 30°
- c)65° and 25°
- d)70° and 30°
Correct answer is option 'C'. Can you explain this answer?
Out of the following options, the two angles that are together classified as complementary angles are
a)
120° and 60°
b)
50° and 30°
c)
65° and 25°
d)
70° and 30°
|
Namita khanna answered |
B)90
c)45
The two angles that are together classified as complementary angles are b)90 and c)45.
c)45
The two angles that are together classified as complementary angles are b)90 and c)45.
If 6cotθ + 2cosecθ = cotθ + 5cosecθ, then cosθ is- a)4/5
- b)5/3
- c)3/5
- d)5/4
Correct answer is option 'C'. Can you explain this answer?
If 6cotθ + 2cosecθ = cotθ + 5cosecθ, then cosθ is
a)
4/5
b)
5/3
c)
3/5
d)
5/4
|
|
Raghav Bansal answered |
6cot+2cosec=cot+5cosec
6cot-cot=5cosec-2cosec
5cot=3cosec
5cos/sin=3/sin
cos=3/5
6cot-cot=5cosec-2cosec
5cot=3cosec
5cos/sin=3/sin
cos=3/5
The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 30° at a point 8m from the foot of the tree. The original height of the tree is- a)8m
- b)24m
- c)24√3m
- d)8√3m
Correct answer is option 'D'. Can you explain this answer?
The upper part of a tree broken by the wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 30° at a point 8m from the foot of the tree. The original height of the tree is
a)
8m
b)
24m
c)
24√3m
d)
8√3m
|
|
Kiran Mehta answered |
If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are- a)15°, 22°
- b)20°, 10°
- c)45°, 15°
- d)30°, 45°
Correct answer is option 'C'. Can you explain this answer?
If 2 cos(A + B) = 1, and 2 sin(A –B) = 1 then the values of A and B are
a)
15°, 22°
b)
20°, 10°
c)
45°, 15°
d)
30°, 45°
|
|
Rohit Sharma answered |
2 cos(A + B) = 1
cos(A + B) = ½
cos(A + B)=cos 60
A+B=60 …(1)
2 sin(A – B) = 1
sin(A - B)=½
sin(A - B)=sin 30
A-B = 30 …(2)
Adding 1 and 2
2A = 90
A = 45
B = 15
cos(A + B) = ½
cos(A + B)=cos 60
A+B=60 …(1)
2 sin(A – B) = 1
sin(A - B)=½
sin(A - B)=sin 30
A-B = 30 …(2)
Adding 1 and 2
2A = 90
A = 45
B = 15
Ratios of sides of a right triangle with respect to its acute angles are known as- a)trigonometric identities
- b)trigonometry
- c)trigonometric ratios of the angles
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Ratios of sides of a right triangle with respect to its acute angles are known as
a)
trigonometric identities
b)
trigonometry
c)
trigonometric ratios of the angles
d)
none of these
|
Ishan Choudhury answered |
The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
If angle A is acute and cos A = 8/17 then cot A is :- a)8/15
- b)17/8
- c)15/8
- d)17/15
Correct answer is option 'A'. Can you explain this answer?
If angle A is acute and cos A = 8/17 then cot A is :
a)
8/15
b)
17/8
c)
15/8
d)
17/15
|
Pooja Shah answered |
Cos A=8/17=B/H
base=8x, hypotenuse=17x
By pythagoras theorem,
H2 =P2 + B2
289x2 = P2 + 64x2
Cot A=B/P=8x/15x=8/15
base=8x, hypotenuse=17x
By pythagoras theorem,
H2 =P2 + B2
289x2 = P2 + 64x2
Cot A=B/P=8x/15x=8/15
If the angle of elevation of a cloud from a point 60 metres above a lake is 30o and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
- a)30 m
- b)120 m
- c)200 m
- d)500 m
Correct answer is option 'B'. Can you explain this answer?
If the angle of elevation of a cloud from a point 60 metres above a lake is 30o and the angle of depression of its reflection in the lake is 60°, then the height of the cloud above the lake is
a)
30 m
b)
120 m
c)
200 m
d)
500 m
|
Neha Patel answered |
Let AB be the surface of the lake and P be the point of observation such that AP = 60 m. Let C be the position of the cloud and C be its reflection in the lake.
Then CB =
Draw PM⊥CB
Let CM = h
∴ CB = h + 60 m
The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:- a)45°
- b)60°
- c)30°
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree, is:
a)
45°
b)
60°
c)
30°
d)
None of these
|
|
Ananya Das answered |
Consider the diagram shown above where QR represents the tree and PQ represents its shadow
We have, QR = PQ
Let ∠QPR = θ
tan θ = QR/PQ = 1 (since QR = PQ)
⇒ θ = 45°
Let ∠QPR = θ
tan θ = QR/PQ = 1 (since QR = PQ)
⇒ θ = 45°
i,e., required angle of elevation = 45°
7 sin2 θ + 3 cos2 θ = 4 then :- a)tan θ = 1/√2
- b)tan θ = 1/2
- c)tan θ = 1/3
- d)tan θ = 1/√3
Correct answer is option 'D'. Can you explain this answer?
7 sin2 θ + 3 cos2 θ = 4 then :
a)
tan θ = 1/√2
b)
tan θ = 1/2
c)
tan θ = 1/3
d)
tan θ = 1/√3
|
|
Nirmal Kumar answered |
7Sin²A+3Cos²A=4,
3Cos²A+3Sin²A+4Sin²A=4,
3(sin²A+Cos²A)+4sin²A=4,
4Sin²A=1,
sin²A=1/2×1/2,
SinA=1/2=Sin 30,
A=30,
tanA=tan30=1/√3
3Cos²A+3Sin²A+4Sin²A=4,
3(sin²A+Cos²A)+4sin²A=4,
4Sin²A=1,
sin²A=1/2×1/2,
SinA=1/2=Sin 30,
A=30,
tanA=tan30=1/√3
A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45o. Then the height (in meters) of the tower is- a)25
- b)25√3
- c)12.5
- d)25√2
Correct answer is option 'A'. Can you explain this answer?
A tower stands vertically on the ground. From a point on the ground which is 25 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 45o. Then the height (in meters) of the tower is
a)
25
b)
25√3
c)
12.5
d)
25√2
|
|
Vikram Kapoor answered |
A point on the ground which is 25 m away from the foot of the tower i. BC= 25 m
Let the height of the tower be x
The angle of elevation of the tower is found to be 45 degree.i.e.∠ACB=45°
In ΔABC
Using trigonometric ratios
Hence the height of the tower is 25 m.
Hence the height of the tower is 25 m.
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