cos(A−B) =
- cosAcosB−sinAsinB
- cosAcosB+sinAsinB
- cosAsinB+sinAcosB
- cosAsinB−sinAcosB
Show answer and explanation
Answer: B. cosAcosB+sinAsinB
Standard angle-difference identity for cosine.
FSC Mathematics: Trigonometric Identities, questions with answers
Practise 30 real Federal Board questions on Trigonometric Identities from 2023 to 2026. See the answer and explanation as soon as you answer.
30real questions
10multiple choice
5exam sessions
About Trigonometric Identities in FSC Mathematics
Trigonometric Identities is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (11th class), and about 6% of its real questions come from it. Tayyari Karo has 30 real questions on this chapter from 2023 to 2026; 10 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 20 medium, 7 hard, 3 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
Using product to sum or difference formula sin60°sin30° =
- √3/4
- √3/2
- 1
- −1
Show answer and explanation
Answer: A. √3/4
sinAsinB=½[cos(A−B)−cos(A+B)]=½[cos30°−cos90°]=½(√3/2)=√3/4.
The expression sin75°cos15° is equivalent to:
- ½(sin90°+sin60°)
- ½(cos90°+cos60°)
- ½(sin60°−sin90°)
- ½(cos60°−cos90°)
Show answer and explanation
Answer: A. ½(sin90°+sin60°)
sinAcosB=½[sin(A+B)+sin(A−B)] ⇒ ½[sin90°+sin60°].
sin(π/3)cos(π/6) =
- 1/4
- √3/2
- √3/4
- 3/4
Show answer and explanation
Answer: D. 3/4
(√3/2)(√3/2)=3/4.
Which of the given options states a solution of Sinx + Cosx = 0, ∀n ∈ Z⁺?
- π/6
- 2π/3
- π/4
- 3π/4
Show answer and explanation
Answer: D. 3π/4
At x = 3π/4: Sin(3π/4)+Cos(3π/4) = √2/2 − √2/2 = 0, so 3π/4 satisfies the equation.
If Cosβ = 3/4, then value of Cos2β is:
- 3√7/8
- −3√7/8
- 1/8
- −1/8
Show answer and explanation
Answer: C. 1/8
Cos2β = 2Cos²β − 1 = 2(9/16) − 1 = 18/16 − 1 = 1/8.
Verify the identity: cos3α=4cos³α−3cosα
Show model answer
cos3α = cos(2α+α) = cos2αcosα − sin2αsinα
= (2cos²α−1)cosα − 2sin²αcosα = 2cos³α−cosα−2(1−cos²α)cosα
= 2cos³α−cosα−2cosα+2cos³α
= 4cos³α−3cosα, verified.
Verify that cos²θ−sin²θ=cos2θ for θ=π/6
Show model answer
cos(π/6)=√3/2, sin(π/6)=1/2
cos²θ−sin²θ = 3/4−1/4 = 1/2
cos2θ = cos(π/3) = 1/2
LHS = RHS = 1/2, verified.
Sessions with Trigonometric Identities questions
| Session | Questions |
|---|---|
| 2026 Annual | 6 |
| 2025 1st Annual | 7 |
| 2025 2nd Annual | 7 |
| 2024 Annual | 5 |
| 2023 Annual | 5 |
Common questions
What does the Trigonometric Identities chapter cover on this page?
30 real Federal Board (FBISE) Mathematics questions on Trigonometric Identities from 2023 to 2026, for 11th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.