Prove the following identities :
1 – 2sin2θ + sin4θ = cos4θ
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Prove the following identities :
1 – 2sin2θ + sin4θ = cos4θ
Prove the following identities :
1 – 2sin2θ + sin4θ = 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