Q. 17

# Prove the followi

To prove: cos 4x = 1 – 8 cos2 x + 8 cos4 x

Proof:

Take LHS:

cos 4x

Identities used:

cos 2x = = 2 cos2 x – 1

Therefore,

= 2 cos2 2x – 1

= 2(2 cos2 2x – 1)2 – 1

= 2{(2 cos2 2x}2 + 12 – 2×2 cos2 x} – 1

= 2(4 cos4 2x + 1 – 4 cos2 x) – 1

= 8 cos4 2x + 2 – 8 cos2 x – 1

= 8 cos4 2x + 1 – 8 cos2 x

= RHS

Hence Proved

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