Question

Please help me do 9c fast please ​

Answer 1

see explanation

Explanation:

Using double angle formulae for cosine and sine

Consider left side

cos4θ

= cos2(2θ)

= cos²(2θ) - sin²(2θ)

= [ cos²θ - sin²θ ]² - (2sinθcosθ)²

= [ (1 - sin²θ - sin²θ ]² - (2sinθcosθ)²

= (1 - 2sin²θ )² - (2sinθcosθ)²

= 1 + 4
`sin^(4)`θ - 4sin²θ - 4sin²θcos²θ

= 1 + 4
`sin^(4)`θ - 4sin²θ - 4(1 - sin²θ)sin²θ

= 1 + 4
`sin^(4)`θ - 4sin²θ - 4sin²θ + 4
`sin^(4)`θ

= 1 - 8sin²θ + 8
`sin^(4)`θ

= right side , thus proven