Answer:
see explanation
Step-by-step 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[tex]sin^{4}[/tex]θ - 4sin²θ - 4sin²θcos²θ
= 1 + 4[tex]sin^{4}[/tex]θ - 4sin²θ - 4(1 - sin²θ)sin²θ
= 1 + 4[tex]sin^{4}[/tex]θ - 4sin²θ - 4sin²θ + 4[tex]sin^{4}[/tex]θ
= 1 - 8sin²θ + 8[tex]sin^{4}[/tex]θ
= right side , thus proven
