求证:(1+sin 2α)/(2cos^2 α+sin 2α)=(1/2)tan α+(1/2)

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求证:(1+sin 2α)/(2cos^2 α+sin 2α)=(1/2)tan α+(1/2)

见图片~

(1+sin 2α)/(2cos^2 α+sin 2α)
=(sin^2α+cos^2α+sin 2α)/(2cos^2 α+sin 2α)
=(sinα+cosα)^2/2cosα(sinα+cosα)
=(sinα+cosα)/2cosα
=(1/2)tan α+(1/2)

答:
(1+sin2α)/(2cos^2α+sin2α)
=[(cos^2α+sin^2α)+2sinαcosα]/(2cos^2α+2sinαcosα)
=(cosα+sinα)^2/[2cosα(cosa+sinα)]
=(cosα+sina)/(2cosα)
=(1/2)tanα+(1/2)