30 SSC CGL Trigonometry MCQs:Powerful Questions for Success

Practice 30 SSC CGL Trigonometry MCQs with answers, detailed explanations, shortcuts, and Tier I & Tier II level questions for faster exam preparation

SSC CGL Trigonometry MCQs

1. If sin θ = 3/ 5 , where θ  is acute, then tan θ:

A) 3/4       B) 4/3

C) 3/5        D) 5/4

Correct Answer: A) 3/4

 Explanation: 

Given sin θ = 3/ 5

Using a right triangle

Perpendicular = 3

Hypotenuse = 5

Base = √(5² –3²) = √16 =4

tan θ =3/4

2. If tan θ = 5/12, then sec θ is:

A) 12/13      B) 13/12

C) 5/13        D) 13/5

Correct Answer: B) 13/12

Explanation: 

We know that 1+ tan² θ = sec² θ

sec² θ = 1+ 25/144

= 169/ 144

sec θ = 13/ 12

3. The value of sin30⁰ cos60⁰ + cos30⁰ sin60⁰ is:

A)  0    B) 1/2

C) 1    D) √3/2

Correct Answer: C) 1

Explanation:  

sin A cos B + cos A sin B= sin(A+B)

sin30⁰ cos60⁰ + cos30⁰ sin60⁰ = sin (60⁰ + 30⁰)

= sin90⁰

=1

4. If cot θ = 7/24, then cosec θ is:

A) 24/25     B) 25/24

C) 7/25      D) 25/7

Correct Answer: B) 25/24

Explanation: 

cot θ = 7/ 24

perpendicular = 24 and base = 7

Hypotenuse =  √(7² + 24²)

= √625

= √25

cosec θ = 25/ 24

5. What is the value of   ?

A) 0       B) 1

C) 2        D)3

Correct Answer: B) 1

Explanation: 

We know that 1– cos² θ = sin² θ

= 1

SSC CGL Trigonometry MCQs

6. If tan A = 1 and A is acute, then A equals:

A)  30°    B)   45°

C)   60°    D)   90°

Correct Answer: B) 45°

Explanation: 

tan A = 1

tan A = tan45⁰

A = 45⁰

7. The value of sec² 45⁰   –  tan² 45⁰ is:

A)  0    B)   1

C)   2    D)   √2

Correct Answer: B) 1

Explanation: 

We know that  sec²θ – tan²θ =1

sec² 45⁰   –  tan² 45⁰ = 1

8. If sin A= cos 30 , where A is acute, then A is:

A)  30°    B)   45°

C)   60°    D)   90°

Correct Answer: C) 60°

Explanation: 

sin (90 – θ) = cos θ

cos30 = sin(90 – 30) = sin60

sin A= sin60

Since A is acute

A = 60

9. If A + B = 90, then which of the following is always true?

A) sin A = sin B    B) tan A = tan B

C) sin A = cos B     D) cos A = cos B

Correct Answer: C) sin A= cos B

Explanation: 

A + B = 90

A = 90 – B

sin A = sin (90 – B)

= cos B

10. If tan θ + cot θ = 2, then the value of tan θ is

A) 1       B) 2

C) 1/2    D) 0

Correct Answer: A) 1

Explanation: 

Let x= tan θ

tan θ + cot θ = 2

tan θ + 1/tan θ = 2

x + 1/x = 2

x ² + 1= 2x

x ²– 2x+1=0

(x– 1)²= 0

x = 1

∴ tan θ = 1

SSC CGL Trigonometry MCQs

11. The value of sin60/cos30is:

A) 1/2      B) 1

C) √3      D) 2

Correct Answer: B) 1

Explanation:  

sin60 = √3/2 and cos30 = √3/2

sin60/cos30 = (√3/2)/ (√3/2 )

= 1

SSC CGL Trigonometry MCQs

12. If sin θ + cos θ = √2 then θ, where (0 < θ < 90  ), is

A) 30°        B) 45°

C) 60°        D) 90°

Correct Answer: B) 45°

Explanation:  

sin 45⁰ + cos 45⁰ = (1/√2) + (1/√2)

= 2/√2

= √2

∴ θ =45

13. If tan θ = 3/4, find

A) – 7        B) 7

C) 1/7       D) – 1/7

Correct Answer: A) – 7

Explanation: 

Given:

tan θ =  3/4

sin θ = 3/5, cos θ =  4/5

14. The value of  is:

A) tan² θ    B) cot ² θ

C)   1         D) tan θ

Correct Answer: A) tan ² θ

Explanation: 

We know that

1+ tan ² θ = sec ² θ, 1+ cot ² θ = cosec ² θ

= tan ² θ

15. If sec θ + tan θ =3, then sec θ – tan θ is

A) 1/3       B) 3

C) 2/3        D) 1

Correct Answer: A) 1/3

Explanation: 

sec² θ – tan² θ = 1

(sec θ + tan θ) (sec θ – tan θ) = 1

3 (sec θ – tan θ) = 1

sec θ – tan θ = 1/3

SSC CGL Trigonometry MCQs

16. If sin θ =  5/13, then  =

A) 25             B) 14

C) 26               D) 5

Correct Answer: A) 169/144

  Explanation: 

sin θ =   5/13

cos θ =   12/ 13

= 25

17. If tan A =1/2 and tan B =1/3, then tan(A+B) is

A)  1         B)   5/6

C)   1/2     D)   6/5

Correct Answer: A) 1

Explanation: 

= 1

18. If A + B = 45, tan A=2, then tan B is

A) –1/3       B) 1/2

C) 2/3        D) – 3

Correct Answer: A) –1/3

Explanation:

tan (A + B) = tan45   =1

1 – 2 tan B = 2 + tan B

1 – 2 = 2 tan B + tan B

– 1 = 3 tan B

tan B =– 1/3

19. A pole casts a shadow of length 10√3 m when the angle of elevation of the sun is 30⁰. Find the height of the pole.

A) 10 m      B) 20 m

C) 30 m      D)15 m

Correct Answer: A) 10 m

Explanation: 

Let height be h)

tan30   =   h/10√3

1/√3 = h/10√3

h = 10m

20. From a point on the ground, the angle of elevation of the top of a 20 m high tower is 45⁰. Find the distance of the point from the foot of the tower.

A)10 m    B) 20 m    C) 20√3 m    D) 40 m

Correct Answer: B) 20 m

Explanation:

Let horizontal distance be x

tan 45° = 20/ x

1 = 20/ x

x = 20

SSC CGL Trigonometry MCQs

21. A man observes the top of a tower at an angle of elevation of 30⁰. After moving 20m towards the tower, the angle becomes 60⁰. The height of the tower is

A)10 m    B)10√3 m    C) 20√3 m    D) 30 m

Correct Answer: B) 10√3 m

Explanation: 

Let the initial distance be x and tower height be h

From the first position

Tan60   =   h/ x

h= √3 x

From the second position

Tan30   =   h/( x + 20)

h√3 =  x +20

(√3x) √3  =  (x +20)

3x = x + 20

2x = 20

x=10

∴ h = 10√3

22. If cos θ = 8/17 , where θ is acute, then sin θ + tan θ is

A)  15/17 + 15/8    B)   15/17 + 8/15

C)   8/17 + 15/8    D)   15/8

Correct Answer: A) 15/17 + 15/8

Explanation: 

Given  cos θ = 8/17

sin θ = 15/17

tan θ = 15/ 8

sin θ + tan θ = 15/17 +15/ 8

23. The value of sin⁴ θ + cos⁴θ when θ =45 is

A)1/2        B)1

C)1/4         D) ¾

Correct Answer: A) 1/2

Explanation: 

sin45   = cos45   =  1/√2

sin⁴ θ + cos⁴θ = (1/√2)⁴ + (1/√2)⁴

= 1/4 + 1/4

24. If sin θ = 3/5, find sin³ θ + cos³ θ, where θ is acute.

A) 63/125   B) 91/125

C) 117/125    D) 72/125

Correct Answer: B) 91/125

Explanation:

Given sin θ = 3/5

cos θ =  4/5

sin³ θ + cos³ θ = (3/5)³ + (4/5)³

= 27/125 + 64/125

= 91/125

25. If tan θ + sec θ = 5, then tan θ is

A) 12/5   B) 24/5

C) 5/2    D) 25/12

Correct Answer: B) 24/5

Explanation: 

We know that (sec θ + tan θ) (sec θ – tan θ) =1

sec θ + tan θ =5

sec θ – tan θ = 1/5

Subtract

(sec θ + tan θ)– (sec θ – tan θ) = 5 – 1/5=   24/ 5

SSC CGL Trigonometry MCQs

26. If A = B = 45⁰, then (1+ tan A) (1+ tan B) equals to

A) 1       B) 2

C) 4        D) 0

Correct Answer: C) 4

Explanation: 

Given A = B = 45⁰

(1+ tan A) (1+ tan B) = (1+ tan 45⁰) (1+ tan 45⁰)

= (1 + 1) (1 + 1)

= (2) (2) = 4

27. The value of  is

A) 1/√3   B) 1    C) √3    D) 2

Correct Answer: A) 1/√3

Explanation: 

= tan (60 – 30)

= tan 30

=1/√3

28. A ladder 10 m long rests against a vertical wall. If its foot is 6 m from the wall, the height reached by the ladder is

A) 6 m   B) 7 m

C) 8 m    D) 9 m

Correct Answer: C) 8 m

Explanation: 

The ladder forms a right triangle

Hypotenuse = 10 m

Base = 6 m

h² = 10² – 6²

= 100 – 36 = 64

h =8

∴ height = 8 m.

 29. If x= sin θ + cos θ, then x² is equal to

A) 1+ sin2 θ   B) 1– sin2 θ

C) 1+ cos2 θ   D)2+ sin2 θ

Correct Answer: A)1+ sin2 θ

Explanation:   

x ² = (sin θ + cos θ )²

= sin² θ + cos² θ +2 sin θ cos θ

x ²=1 + sin2 θ [ 2 sin θ cos θ = sin2 θ]

30. A tower is observed from a point on the ground at an angle of elevation of 60⁰. If the point is 15 m from the foot of the tower, the height of the tower is

A)15 m    B)15√3 m    C) 30 m    D) 45 m

Correct Answer: B) 15√3 m

Explanation: 

Let height be h

tan60 = h/15

√3 = h/15

h=15√3 m

SSC CGL Trigonometry MCQs

SSC CGL Quantitative Aptitude Topics

• Number System
• Decimals
• Fractions
• Percentages
• Ratio & proportion
• Square roots
• Averages
• Interest (simple & compound)
• Profit & loss
• Discount
• Partnerships
• Mixture & Alligation
• Time & speed & distance
• Time & work
• Advanced math includes basic algebraic identities
• Elementary surds
• Linear equations
• Triangles
• Circles
• Regular polygons, right prisms, cones, cylinders, spheres
• Trigonometry

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