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1. |
Prove the following identities :(sinθ – cosθ)2 = 1 – 2 sinθ . cosθ |
Answer» Taking LHS = (sin θ – cos θ)2 Using the identity,(a – b)2 = (a2 + b2 – 2ab) = sin2 θ + cos2 θ – 2sin θ cos θ = 1 – 2sin θ cos θ [∵ cos2 θ + sin2 θ = 1] = RHS Hence Proved |
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