Question

sinθ(1+sin2θ)=cos2θ then prove that cos6θ-4cos4θ+8cos2θ=4. please answer​

Answer 1

Answer:

ANSWER

Given : sinθ+sin2θ+sin3θ=1

sinθ(1+sin2θ)=1−sin2θ=cos2θ

⇒1−cos2θ(2−cos2θ)=cos2θ

Squaring both sides, we have

(1−cos2θ)(4+cos4θ−4cos2θ)=cos4θ

⇒cos6θ−4cos4θ+8cos2θ=4

Hence proved