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Question

Prove that: sin2(π/8A/2)sin2(π/8A/2)=12sinA

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Solution

Using
sin2Asin2B=sin(A+B)sin(AB)
we get
LHS =sin(π/8+A/2+π/8A/2)sin(π/8+A/2π/8A/2)=sin(π/4)sinA=(1/2)sinA= RHS

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