9.4) =
show that: 4sinθcos^3θ - 4cosθ sin^3θ =
sin4θ
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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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