Prove : cos4x = 1 - 8cos²x + 8 cos^4 x
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Step-by-step explanation:
Cos4x = Cos(2*2x)
= 2Cos²2x - 1
= 2(2Cos²x-1)² - 1
= 2(4Cos⁴x-4Cos²x+1) - 1
= 8Cos⁴x - 8Cos²x + 2 - 1
= 1 - 8Cos²x + 8Cos⁴x
Ahead from here
= 1 - 8Cos²x(1-Cos²x)
= 1 - 8Cos²x*Sin²x
= 1 - 2(4Sin²x*Cos²x)
= 1 - 2Sin²2x
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