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Question

If tanθ=sinαcosαsinα+cosα, then show that sinα+cosα=2cosθ.

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Solution

tanθ=sinαcosαsinα+cosα
tanθ=tanα1tanα+1
tanθ=tanαtanπ41+tanπ4.tanαtanθ=tan(απ4)
θ=απ4
cosθ=cos(απ4)
cosθ=cosα.cosπ4+sinα.sinπ4cosθ=cosα.12+sinα.12
cosθ=cosα+sinα22cosθ=sinα+cosα
Hence proved.

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