Cos (4theta) = cos^4 - 6sin^2cos^2 + sin^4

Question

Cruz Orr

Mathematics

8 August, 18:44

Cos (4theta) = cos^4 - 6sin^2cos^2 + sin^4

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Sawyer Walters · Answer 1

Cos (4x) = cos (2x+2x)

= cos² (2x) - sin² (2x)

= [cos (x+x) ]²-[sin (x+x) ]²

= [cos²x-sin²x]²-4sin² (x) cos² (x)

= cos⁴ (x) - cos² (x) sin² (x) - cos² (x) sin² (x) + sin⁴ (x) - 4sin² (x) cos² (x)

= cos⁴ (x) - 6sin² (x) cos² (x) + sin⁴ (x)