1.

Prove the following identities :1 – 2 cos2θ + cos4θ = sin4θ

Answer»

Taking LHS = 1 – 2 cos2 θ + cos4 θ

We know that,

cos2 θ + sin2 θ = 1

= 1– 2 cos2 θ + (cos2 θ)2

= 1 – 2 cos2 θ + (1 – sin2 θ)2

= 1 – 2 cos2 θ +1 + sin4 θ – 2sin2θ

= 2 – 2(cos2 θ + sin2θ) + sin4 θ

= 2 – 2(1) + sin4 θ

= sin4 θ

= RHS

Hence Proved



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