Q15 of 268 Page 5

Prove the following identities :

1 – 2 sin2 θ + sin4 θ = cos4θ

Taking LHS = 1 – 2 sin2 θ + sin4 θ

We know that,


cos2 θ + sin2 θ = 1


= 1– 2 sin2 θ + (sin2 θ)2


= 1 – 2 sin2 θ + (1 – cos2 θ)2


= 1 – 2 sin2 θ +1 + cos4 θ – 2cos2θ


= 2 – 2(cos2 θ + sin2θ) + cos4 θ


= 2 – 2(1) + cos4 θ


= cos4 θ


=RHS


Hence Proved


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