FSc Part 1 Maths chapter 10: Trigonometric identities MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

19 exam-style questions on Trigonometric identities, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

19 questions · 2 topics · 10 per test

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What chapter 10 covers

Ten Trigonometric identities questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. sin P + sin Q is equal to

  1. A
    2 cos((P + Q)/2) cos((P − Q)/2)
  2. B
    2 cos((P + Q)/2) sin((P − Q)/2)
  3. C
    2 sin((P + Q)/2) cos((P − Q)/2)
  4. D
    sin(P + Q)
Show answer

Answer: C. sin P + sin Q = 2 sin((P + Q)/2) cos((P − Q)/2). The second option is sin P − sin Q and the third is cos P + cos Q.

2. The value of 2 cos215° − 1 is

  1. A
    1
  2. B
    1/2
  3. C
    √3/2
  4. D
    √3
Show answer

Answer: C. 2 cos2θ − 1 = cos 2θ, so the expression is cos 30° = √3/2.

3. sin 3θ is equal to

  1. A
    3 sin θ − 4 sin3θ
  2. B
    4 sin3θ − 3 sin θ
  3. C
    3 sin θ + 4 sin3θ
  4. D
    3 cos θ − 4 cos3θ
Show answer

Answer: A. sin 3θ = 3 sin θ − 4 sin3θ, while cos 3θ = 4 cos3θ − 3 cos θ; the order of the terms is reversed between them.

4. α and β are acute angles with sin α = 3/5 and cos β = 5/13. Then sin(α + β) is

  1. A
    −16/65
  2. B
    33/65
  3. C
    56/65
  4. D
    63/65
Show answer

Answer: D. cos α = 4/5, sin β = 12/13. sin(α + β) = (3/5)(5/13) + (4/5)(12/13) = 15/65 + 48/65 = 63/65. 56/65 is cos(α − β).

5. cos 2θ in terms of sin θ only is

  1. A
    2 sin2θ − 1
  2. B
    1 − 2 sin2θ
  3. C
    1 + 2 sin2θ
  4. D
    1 − sin2θ
Show answer

Answer: B. cos 2θ = cos2θ − sin2θ = (1 − sin2θ) − sin2θ = 1 − 2 sin2θ.

6. The exact value of cos 75° + cos 15° is

  1. A
    √6/4
  2. B
    √2/2
  3. C
    √3/2
  4. D
    √6/2
Show answer

Answer: D. cos P + cos Q = 2 cos((P + Q)/2) cos((P − Q)/2) = 2 cos 45° cos 30° = 2(√2/2)(√3/2) = √6/2 ≈ 1.225.

7. The value of tan 315° is

  1. A
    −1
  2. B
    1
  3. C
    −√3
  4. D
    √3
Show answer

Answer: A. tan 315° = tan(360° − 45°) = −tan 45° = −1, since tangent is negative in quadrant IV.

8. cos(α + β) is equal to

  1. A
    cos α cos β + sin α sin β
  2. B
    cos α cos β − sin α sin β
  3. C
    sin α cos β + cos α sin β
  4. D
    cos α + cos β
Show answer

Answer: B. For the sum the sign changes: cos(α + β) = cos α cos β − sin α sin β. sin α cos β + cos α sin β is sin(α + β).

9. If cos θ = 1/2, the triple-angle formula gives cos 3θ equal to

  1. A
    1
  2. B
    −1
  3. C
    0
  4. D
    −1/2
Show answer

Answer: B. cos 3θ = 4 cos3θ − 3 cos θ = 4(1/8) − 3/2 = 1/2 − 3/2 = −1. Check: θ = 60° gives cos 180° = −1.

10. sin(180° − θ) is equal to

  1. A
    −sin θ
  2. B
    sin θ
  3. C
    cos θ
  4. D
    −cos θ
Show answer

Answer: B. 180° − θ is in quadrant II (for acute θ), where sine is positive, and a multiple of 180° keeps the same function: sin θ.

Start the chapter testAbout the FSc Part 1 Maths test

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Ways to practise this chapter

Trigonometric identities: questions students ask

How many Trigonometric identities MCQs are there?

19, each with the answer and a short explanation, across 2 topics: Compound and allied angles, Double, half and triple angles; sums and products. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 10 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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