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