Elective Mathematics

Question 1

1cos 2θ can be written as

Easy

A. sin²θ − cos²θ B. 2 sin θ cos θ C. 1 − 2 sin²θ D. 1 + 2 sin²θ

Question 2

2Simplify sin 2θ / (1 + cos 2θ).

Hard

A. tan θ B. 2 tan θ C. sin θ D. cot θ

Question 3

3Prove that (1 − cos 2θ)/sin 2θ equals

Hard

A. tan θ B. cot θ C. cos θ D. sin θ

Question 4

4sin(A + B) =

Easy

A. sin A + sin B B. sin A cos B + cos A sin B C. sin A sin B + cos A cos B D. cos A cos B − sin A sin B

Question 5

5cos²θ − sin²θ is equal to

Easy

A. 1 B. sin 2θ C. cos 2θ D. tan 2θ

Question 6

6sin 2θ is equal to

Easy

A. sin²θ − cos²θ B. 1 − 2 sin θ C. 2 sin θ D. 2 sin θ cos θ

Question 7

7sin²θ + cos²θ =

Easy

A. 1 B. tan θ C. 2 D. 0

Question 8

8tan 2θ =

Easy

A. 2tan θ B. tan²θ C. 1/(1 + tan²θ) D. 2tan θ/(1 − tan²θ)

Question 9

9If tan A = 1/2 and tan B = 1/3, find A + B.

Hard

A. 30° B. 90° C. 60° D. 45°

Question 10

10Which identity is always true?

Easy

A. sin θ + cos θ = 1 B. 1 + sin²θ = cos²θ C. tan θ = cos θ ÷ sin θ D. 1 + tan²θ = sec²θ