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Question

Show that
cos2θcos2ϕ+sin2(θϕ)sin2(θ+ϕ)=cos(2θ+2ϕ)

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Solution

LHS=cos2θcos2ϕ+sin2(θϕ)sin2(θ+ϕ)=cos2θcos2ϕsin(θϕ+θ+ϕ)sin(θϕθϕ)=cos2θcos2ϕ+sin2θsin2ϕ=cos(2θ+2ϕ)=RHS

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