证明恒等式,(sin2α/1+cos2α)(cosα/1+cosα)=tanα/2.
问题描述:
证明恒等式,(sin2α/1+cos2α)(cosα/1+cosα)=tanα/2.
答
(sin2α/1+cos2α)(cosα/1+cosα)=tanα/2.
(2sinacosa/(cos²a+sin²a+cos²a-sin²a))(cosa/(1+cosa))
sina/cosa×cosa/(1+cosa)
=sina/(1+cosa)
=2sina/2cosa/2/(cos²a/2+sin²a/2+cos²a/2-sin²a/2)
=2sina/2cosa/2/(2cos²a/2)
=tana/2;
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