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9.4) =show that: 4sinθcos^3θ - 4cosθ sin^3θ =sin4θ |
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Answer» Step-by-step EXPLANATION: To PROVE : 4sinθcos³θ - 4cosθ sin³θ = sin4θ take LHS = 4sinθcos³θ - 4cosθ sin³θ = 2sinθcosθ (2cos²θ-2sin²θ) = sin2θ. 2 .(cos²θ - sin²θ) [ ∵ sin2θ = 2sinθcosθ ] = 2 sin2θ cos2θ [ ∵ cos2θ = cos²θ - sin²θ ] = sin2(2θ) = sin4θ = RHS => LHS = RHS. Hence proved |
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