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Prove the following identities: cos 4x = 1 – 8 cos^2 x + 8 cos^4 x

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Prove the following identities:

cos 4x = 1 – 8 cos2x + 8 cos4x

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Best answer

To prove: cos 4x = 1 – 8 cos2x + 8 cos4x

Proof:

Take LHS:

cos 4x

Identities used:

cos 2x = = 2 cos2x – 1

Therefore,

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