Question

If theta and (2theta+ 45°) are acute angles such that sin theta = cos(2theta+ 45°), then root 2sin 3theta – 2tan 3theta is equal to
(a) 0
(b) -1
(0) 1
(d) 2​

Answer 1

(b) -1

Explanation:

Sin θ = Cos (2θ + 45°)

= Sin (90° - (2θ + 45°))

= Sin (45° - 2θ)

So θ = 45° - 2θ

3θ = 45°

Therefore θ = 15°

Now ✓2 sin 3θ – 2tan 3θ = ✓2 sin 3(15°) – 2tan 3(15°)

= ✓2 sin 45° – 2tan 45°

= ✓2 * 1/✓2 - 2 * 1

= 1 - 2

= -1

Option B is the answer.