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SSC CGL Exam  >  SSC CGL Tests  >  SSC CGL Previous Year Papers  >  SSC CGL Previous Year Questions: Trigonometry - 4 - SSC CGL MCQ

SSC CGL Previous Year Questions: Trigonometry - 4 - SSC CGL MCQ


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30 Questions MCQ Test SSC CGL Previous Year Papers - SSC CGL Previous Year Questions: Trigonometry - 4

SSC CGL Previous Year Questions: Trigonometry - 4 for SSC CGL 2024 is part of SSC CGL Previous Year Papers preparation. The SSC CGL Previous Year Questions: Trigonometry - 4 questions and answers have been prepared according to the SSC CGL exam syllabus.The SSC CGL Previous Year Questions: Trigonometry - 4 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for SSC CGL Previous Year Questions: Trigonometry - 4 below.
Solutions of SSC CGL Previous Year Questions: Trigonometry - 4 questions in English are available as part of our SSC CGL Previous Year Papers for SSC CGL & SSC CGL Previous Year Questions: Trigonometry - 4 solutions in Hindi for SSC CGL Previous Year Papers course. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free. Attempt SSC CGL Previous Year Questions: Trigonometry - 4 | 40 questions in 40 minutes | Mock test for SSC CGL preparation | Free important questions MCQ to study SSC CGL Previous Year Papers for SSC CGL Exam | Download free PDF with solutions
SSC CGL Previous Year Questions: Trigonometry - 4 - Question 1
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(3π/5) radians is equal to   (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 1

∵ π radian = 180°

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 2
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Evaluate: 3 cos 80° cosec 10° + 2 cos 59° cosec 31°    (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 2

3 cos 80°. cosec 10° + 2 cos 59°. cosec 31°
= 3 cos (90° – 10°). cosec 10° + 2 cos (90° – 31°). cosec 31°
= 3 sin 10°. cosec 10° + 2 sin 31°. cosec 31° = 3 + 2 = 5
[∵ cos (90° – θ) = sinθ; sinθ.cosecθ = 1]

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SSC CGL Previous Year Questions: Trigonometry - 4 - Question 3
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If the angles of elevation of a balloon from two consecutive kilometre–stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be    (SSC CGL 1st Sit. 2013)

Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 3


SSC CGL Previous Year Questions: Trigonometry - 4 - Question 4
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From 125 metre high towers, the angle of depression of a car is 45°. Then how far the car is from the tower?   (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 4

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 5
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If tan α + cot α = 2, then the value of tan 7α + cot7α is    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 5

tan α + cot α = 2

⇒ tan2 α – 2 tan α + 1 = 0
⇒ tan2 α – tan α – tan α + 1 = 0
⇒ tan α (tan α – 1) – 1 (tan α – 1) = 0 (tan α – 1) (tan α – 1) = 0
∴ tan α = 1

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 6
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If x = a cos θ – b sin θ, y = b cos θ + a sin θ, then find the value of x2 + y2.    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 6

x = a cos θ – b sin θ
y = b cos θ + a sin θ
x2 + y2 = (a cos θ – b sin θ)2 + (b cos θ + a sin θ)2 = a2 cos2 θ + b2 sin2 θ + a2 sin2 θ + b2 cos2 θ
= a2 + b2

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 7
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In a triangle, the angles are in the ratio 2 : 5 : 3. What is the value of the least angle in the radian?    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 7

Let angles are 2x, 5x and 3x.
2x + 5x + 3x = 180º (sum of interior angle of triangles is 180º)
10x = 18º
x = 18º
∴ Least angle in degree = 2x = 2 × 18 = 36º

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 8
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The value of    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 8

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 9
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The value of    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 9

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 10
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The value of     (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 10


[∵ cos (90º – θ) = sin θ and cot (90º – θ) = tan θ]

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 11
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If cos4θ – sin4θ = 2/3, then the value of 1 – 2 sin2θ is    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 11

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 12
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If cosθ + sinθ = √2 cos θ, then cosθ – sinθ is    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 12

cosθ + sinθ = √2 cos θ
On squaring both sides,
cos2θ + sin2θ + 2cos θ. sin θ = 2 cos2 θ
⇒ cos2θ – sin2θ = 2cosθ. cos θ
⇒ (cos θ + sin θ) (cos θ – sin θ) = 2 sin θ. cos θ
⇒ 2 cos θ (cosθ – sinθ) = 2sin θ. cos θ

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 13
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The value of     (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 13

Expression

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 14
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If tan α = n tan β, and sin α = m sin β, then cos2 α is    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 14



SSC CGL Previous Year Questions: Trigonometry - 4 - Question 15
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The tops of two poles of height 24 m and 36 m are connected by a wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 15


BC = ED = 24 m
∴ AE = AD – ED = 36 m  – 24 m = 12 m
In ΔABE,

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 16
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The value of     (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 16

Expression

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 17
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If tan θ = 3/4 and θ is acute, then cosec θ   (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 17

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 18
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One of the four an gles of a rhombus is 60°. If the length of each side of the rhombus is, 8 cm, then the length of the longer diagonal is    (SSC CGL 2nd Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 18


∠BAD = 60°
∴ ∠BAO = 30°
∠ABO = 60°

∴ OA = 43
∴ AC = 83 metre

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 19
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If (1 + sinα) (1 + sinβ) (1 + sinγ) = (1 – sinα) (1 – sinβ) (1 – sinγ), then each side is equal to   (SSC CGL 2nd Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 19

(1 + sin α) (1 + sin β) (1 + sin γ) = (1 – sin α)  (1 – sin β) (1 – sin γ) = x
∴ x.x = (1 + sin α) (1– sin α) (1 + sin β)
(1 – sin β) (1 + sin γ) (1 – sin γ)
x2 = (1 – sin2 α) (1 – sin2 β) (1 – sin2 γ)
x2 = cos2 α. cos2β.cos2 γ
⇒ x = ± cos α. cos β . cos γ 

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 20
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The value of 152 (sin 30° + 2 cos2 45° + 3 sin 30° + 4 cos2 45° +...+17 sin 30° + 18 cos2 45°) is    (SSC CGL 2nd Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 20

152 (sin 30° + 2 cos2 45° + 3 sin 30° + 4 cos2 45° +...+17 sin 30° + 18 cos2 45°)
   equals space 152 open square brackets 1 half space plus space 2 open parentheses 1 half close parentheses space plus space 3 open parentheses 1 half close parentheses space plus space 4 open parentheses 1 half close parentheses space plus....18 open parentheses 1 half close parentheses close square brackets equals space 152 space cross times space 1 half left square bracket 1 space plus space 2 space plus space 3 space plus space 4 space plus space..... plus 18 right square bracket equals space 152 space cross times space 1 half space cross times space fraction numerator 18 space cross times space 19 over denominator 2 end fraction equals space 76 space cross times space 9 space cross times space 19 space equals space 12996 space equals space left parenthesis 114 right parenthesis squared
Thus, Required number is a perfect square of an integer.

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 21
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Maximum value of (2 sin θ + 3 cos θ) is    (SSC CGL 2nd Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 21

Maximum value of 2 sin θ + 3 cos θ
           equals space square root of left parenthesis 2 right parenthesis squared space plus space left parenthesis 3 right parenthesis squared end root equals space square root of 4 space plus space 9 end root space equals space square root of 13

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 22
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If sin ( A – B ) = 1/2 and cos (A + B) = 1/2 where A > B > 0 and A + B is an acute angle, then the value B is    (SSC CGL 2nd Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 22

sin (A – B) = 1/2 = sin 30° ⇒ A – B= 30°
cos (A + B) = 1/2 = cos 60° ⇒ A + B = 60°
∴ A + B + A – B = 30° + 60° = 90°
⇒ 2A = 90° ⇒ A = 45°
∴ A – B = 30°

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 23
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Evaluate : tan 1° tan 2° tan 3° ........... tan 89°.    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 23

tan 89° = tan (90° – 1°) = cot 1°
tan 88° = tan (90° – 2°) = cot 2°
∴ Expression = tan 1°, cot 1°, tan 2°,  cot2° ... tan 45° = 1
[∵ tan θ. cot θ = 1]

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 24
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If secθ + tanθ = 2 + √5,  then the value of sinθ + cosθ is?   (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 24


SSC CGL Previous Year Questions: Trigonometry - 4 - Question 25
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If sinθ + cosecθ = 2, then sin9θ + cosec9θ is equal to ______.    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 25

sinθ + cosecθ = 2

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 26
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The degree measure of 1 radian (taking π = (22 / 7)) is
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 26

π radian = 180°

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 27
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The value of (sin2 25° + sin2 65°) is:    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 27

sin2 25° + sin2 65°
= sin2 25° + sin2 (90° – 25°)
= sin2 25° + cos2 25° = 1

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 28
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The value of cos 1° cos 2° cos 3°............ cos 177° cos 178° cos 179° is:    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 28

cos 90° = 0
∴ cos 1°, cos 2° .... cos 179° = 0

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 29
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The angle of elevation of a tower from a distance 100 m from its foot is 30°. Height of the tower is:    (SSC CGL 1st Sit. 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 29


AB = h metre
∠ACB = 30°;
BC = 100 metre

SSC CGL Previous Year Questions: Trigonometry - 4 - Question 30
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If 2(cos2θ - sin2θ) = 1, (θ is positive acute angle), then cotθ is equal to?   (SSC CHSL 2013)
Detailed Solution for SSC CGL Previous Year Questions: Trigonometry - 4 - Question 30

2 cos 2θ = 1
cos 2θ = 1/2
θ = 30°
cot 30° = √3

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