Quiz  /  Trigonometry SSC MCQ Questions With Answers

  • 1. 
    If (cotA – tan A)/2 = x, then the value of x is

  • tan2A
  • cot2A
  • tan3A
  • cotA

  • 2. 
    The value of cos225° + cos270° is

  • -√2
  • 2
  • -1/√2
  • 1

  • 3. 
    From a point, 40 m apart from the foot of a tower, the angle of elevation of its top is 60°. The height of the tower is

  • 120√3 m
  • 40/√3 m
  • 40√3 m
  • 40√2 m

  • 4. 
    If cot 60° + cosec 60° = x, then the value of x is

  • (1 - 2√2)/√2
  • (√3 - 4)/2√3
  • 1
  • √3

  • 5. 
    What is the value of tan 6° tan 36° tan 84° tan 54° tan 45°?

  • 1/2
  • 1/√2
  • 1
  • 1/3

  • 6. 
    If tan ∅ = 4/3, then the value of \(\frac{{3\sin \emptyset \; + \;2\cos \emptyset }}{{3\sin \emptyset - 2\cos \emptyset }}\) is

  • 1/2
  • 1 ½
  • 3
  • -3

  • 7. 
    A landmark on the bank of a river are observed from two points A and B on the opposite bank of the river. The lines of sight make equal angles of 30° with the bank of the river. If AB = 3 km, then the width of the river (in kilometre) is

  • (3√2)/2
  • 2
  • √3
  • √3/2

  • 8. 
    What is the value of sin(630 + A) + cosA?

  • √3/2
  • 1/2
  • 0
  • 2/√3

  • 9. 
    What is the value of [sin(90° - A) + cos(180° - 2A)] / [cos(90° - 2A) + sin(180° - A)]?

  • sin(A/2).cosA
  • cot(A/2)
  • tan(A/2)
  • sinA.cos(A/2)

  • 10. 
    What is the value of sin (90° + 2A)[4 - cos2(90° - 2A)]?

  • 2(cos3A - sin3A)
  • 2(cos3A + sin3A)
  • 4(cos6A + sin6A)
  • 4(cos6A - sin6A)

  • 11. 
    A Navy captain going away from a lighthouse at the speed of 4(√3 – 1) m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60° to 45°. What is the height (in metres) of the lighthouse?

  • 240√3
  • 480(√3 – 1)
  • 360√3
  • 280√2

  • 12. 
    What is the simplified value of sec6 A - tan6 A - 3 sec2 A tan2 A?

  • -1
  • 0
  • 1
  • sec A tan A

  • 13. 
    A tree is 70 meters high. Its shadow is x metres shorter when the sun's altitude is 45° than when it is 30°. The value of x in metres is

  • 70√3
  • 70(√3 - 1)
  • 70(√3 + 1)
  • 70

  • 14. 
    The length of shadow of a tower is √3 times that of its length. The angle of elevation of the sun is

  • 45°
  • 30°
  • 60°
  • none

  • 15. 
    What is the simplified value of \({\left( {\frac{1}{{sec\;A\; + \;tan\;A\;}}} \right)^2}\)

  • secA + tanA
  • sinA cosA
  • (1 – sinA)/(1 + sinA)
  • (1 – cosA)/(1 + cosA)

  • 16. 
    The value of sin 10° sin 30° sin50° sin 70° will be -

  • 4/25
  • 1/16
  • 1/8
  • 3/16

  • 17. 
    If cos 11π/6 = x, then the value of x is

  • -√3/2
  • 1/2
  • 2
  • √3/2

  • 18. 
    What is the value of [2cot(π – A)/2] / [1 + tan2(2π – A)/2]?

  • 2sin2A/2
  • cosA
  • sinA
  • 2cos2A/2

  • 19. 
    Two supplementary angles are in the ratio 3:2. The angles are

  • 114°, 66°
  • 108°, 72°
  • 54°, 36°
  • 33°, 57°

  • 20. 
    The value of \({\sec ^2}12^\circ - \frac{1}{{{{\tan }^2}78^\circ }}\) is

  • 0
  • 1
  • 2
  • 3

  • 21. 
    The expression \(\frac{{\tan 67^\circ \; + \;\cot 47^\circ }}{{\tan 23^\circ \; + \;\cot 43^\circ }}\) is equal to

  • tan 67° cot 47°
  • tan 47° cot 67°
  • tan 47° cot 47°
  • tan 67° cot 67°

  • 22. 
    If cot(A/2) = x, then the value of x is?

  • √[(1 + cosA)/(1 - cosA)]
  • cosecA - cotA
  • √[(1 - cosA)/2]
  • √[(1 + cosA)/2]

  • 23. 
    Two poles are ‘a’ meter apart and the height of one is thrice of the other. If from the middle point of line joining their feet, an observer finds the angular elevation of their tops to be complementary then the height of shorter pole is

  • a/3 meter
  • a/√3 meter
  • 2a√3 meter
  • a/(2√3) meter

  • 24. 
    If sinA + sin2A = 1 then what is the value of cos2A + cos4A?

  • ½
  • 1
  • 2
  • 3

  • 25. 
    If \(\cos \frac{\pi }{2}x = {x^2} - 2x + 2\), the value of x will be :

  • 0
  • 1
  • -1
  • None of the above

  • 26. 
    If tan 45° + cosec 30° = x, then find the value of x.

  • √3
  • (1 - 2√2)/√2
  • (√3 - 4)/2√3
  • 3

  • 27. 
    A ladder is placed against a wall such that it just reaches the top of the wall. The foot of the ladder is at a distance of 5 metres from the wall. The angle of elevation of the top of the wall from the base of the ladder is 15°. What is the length (in metres) of the ladder?

  • 5√6 - 5√3
  • 5√6 - 5√2
  • 5√2 - 1
  • 5√3 + 5√2

  • 28. 
    What is the value of [(cos7A + cos5A) / (sin7A – sin 5A)]?

  • tan A
  • tan 4A
  • cot 4A
  • cot A

  • 29. 
    What is the value of [(tan5θ + tan3θ)/4cos4θ (tan5θ – tan3θ)]?

  • sin2θ
  • cos2θ
  • tan4θ
  • cot2θ

  • 30. 
    What is the value of [1 - tan(90° - θ) + sec(90° - θ)]/[tan(90° - θ) + sec(90° - θ) + 1]?

  • cot(θ/2)
  • tan(θ/2)
  • sin θ
  • cos θ
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