Question

If sin - sin² - sin³ = 1 Then, prove that cos⁶ - 4cos² +4 =0​

Answer 1

Given : sinθ+sin

2 θ+sin 3 θ=1

sinθ(1+sin 2 θ)=1−sin 2 θ=cos 2 θ⇒ 1−cos 2 θ

(2−cos 2 θ)=cos 2 θ

Squaring both sides, we have

(1−cos 2θ)(4+cos 4 θ−4cos 2θ)=cos 4 θ

⇒cos 6

θ−4cos 4

θ+8cos 2 θ=4