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Prove that cos 6x = 32 cos6 x – 48cos4 x + 18 cos2 x – 1

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L.H.S

cos6x=cos3(2x)

⇒4cos32x−3cos2x

⇒4(2cos2x−1)3−3(2cos2x−1)

⇒4(8cos6x−12cos4x+6cos2x−1)−6cos2x+3

⇒32cos6x−48cos4x+24cos2x−4−6cos2x+3

⇒32cos6x−48cos4x+18cos2x−1=R.H.S

Hence proved.

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