(2sin²α+2sinα*cosα)/(1+tanα)

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(2sin²α+2sinα*cosα)/(1+tanα)

(2sin²α+2sinαcosα)/(1+tanα)
=2sina(sina+cosa)/(1+sina/cosa)
=2sinacosa(sina+cosa)/(cosa+sina)
=2sinacoas
=sin2a