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Question

If sinθ is G.M of sinϕ and cosϕ, then prove that cos2θ=2cos2(π4+ϕ)

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Solution

sin2θ=sinϕcosϕ
2sin2θ=sin2ϕ
1cos2θ=cos(π/2+2ϕ)
cos2θ=1+cos(π/2+2ϕ)
cos2θ=2cos2(π4+ϕ)

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