Question

Prove that cos 6x = 32 cos^6 x-48 cos^4x + cos^2x-1​

Answer 1

Answer:

Step-by-step explanation:

1). cos²α = $\frac{1+cos2\alpha }{2}$ ⇔ 2cos²α = cos2α + 1 ⇔ cos2α = 2cos²α - 1

2). cos3β = 4cos³β - 3cosβ

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R.H.

cos6x = cos2(3x)

cos2(3x) = 2cos²3x - 1 = 2(cos3x)² - 1

cos2(3x) = 2(4cos³x - 3cos x)² - 1 = 2(16$cos^{6}$x - 24$cos^{4}$x + 9cos²x) - 1 = 32$cos^{6}$x - 48$cos^{4}$x + 18cos²x - 1

Thus,

cos 6x =  32$cos^{6}$x - 48$cos^{4}$x + 18cos²x - 1