If sin A+sin 2 A=1, then the value of (cos 2 A +cos 4 A) is

Question

Philoid · Accepted Answer

Given: sin A ₊ sin² A = 1

⇒ sin A = 1 – sin² A

(By Rearranging)

⇒ sin A = cos² A

(∵, sin² θ +cos² θ =1

⇒ cos² θ = 1 – sin² θ)

Squaring both sides, we get

⇒ sin² A = cos⁴ A or cos⁴ A = sin² A

Thus, cos² A + cos⁴ A = sin A + sin² A = 1 (∵ sin A₊sin² A = 1)

∴ cos² A + cos⁴ A = 1