If sin (60°-θ), sin θ, sin (60°+θ) (taken in that order) are in G.P., then cos 2 θ is equal to

Question

If sin (60°-θ), sin θ, sin (60°+θ) (taken in that order) are in G.P., then cos 2 θ is equal to (A) (1/8) (B) (3/8) (C) (5/8) (D) (7/8)

Tardigrade Admin · Accepted Answer

We have, sin 2 θ= sin 2 60°- sin 2 θ ⇒ 2 sin 2 θ=(3/4) ⇒ sin 2 θ=(3/8) ∴ cos 2 θ=1-(3/8)=(5/8)

Q. If $sin (6 0^{\circ} - θ), sin θ, sin (6 0^{\circ} + θ)$ (taken in that order) are in G.P., then $cos^{2} θ$ is equal to