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