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All questions of Trigonometry for SSS 1 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?

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
Cosθ = Base / Hypotenuse
CosA = 2 / 3.6
Hence the value of Cos A is 2/3.6=2/√13

 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?

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?

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 .

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?

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
We get=
(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.

Amit Kumar answered
7sin2x+3cosx=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+ 

If tan θ = a/b then the value of 
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

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) 

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?

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

 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?

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

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?

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 . 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 

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?

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?

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 

 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?

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?

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.

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?

Amit Sharma answered
cos217-sin273
=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?

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

5 cot2 A – 5 cosec2 A =
  • a)
    – 5
  • b)
    1
  • c)
    0
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?

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

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?

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?

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.

 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?

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

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?

Pooja Shah answered
Cos A=8/17=B/H
base=8x, hypotenuse=17x
By pythagoras theorem,
H=P+ B2
289x= P+ 64x2

Cot A=B/P=8x/15x=8/15

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?

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

If tanθ > 0, sinθ > 0, then the terminal arm of the angle lies in the quadrant
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    4
Correct answer is option 'A'. Can you explain this answer?

Amit Kumar answered
The correct option is Option A.
If the angle is between 0 to 90 degrees then it will lies in the first quadrant.
The tanθ and sinθ have positive values, hence lies in first quadrant.

The value of     is
  • a)
    2
  • b)
    0
  • c)
    4
  • d)
    -2
Correct answer is option 'D'. Can you explain this answer?

Krishna Iyer answered
we know sin(90 - a) = cos(a) 
cos(90 - a) = sin(a)
sin(a) = 1/cosec(a)
sec(a) = 1/cos(a)
 
cos40 = cos(90-50) = sin50
cosec40 = cosec(90-50) = sec50
so our expression becomes
sin50/sin50 + sec50/sec50 - 4cos50 / sin40
= 1 + 1 - 4(1)   since cos50 = sin40
= -2

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