Answer :

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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