Question

怎么证明tan2α=(2tanα)/(1-tan²α)

怎么证明tan2α=(2tanα)/(1-tan²α)
怎么证明tan²α=(1-cos2α)/(1+cos2α)
我需要一步一步的详细过程（明天期末考了帮帮忙>w<）

Answer 1

tan2α=(2tanα)/(1-tan²α)
tan2α
=sin2α/cos2α=2sinαcosα/(cos²α-sin²α)
=[2sinαcosα÷cos²α]/[(cos²α-sin²α)÷cos²α]
=(2tanα)/(1-tan²α)
tan²α=(1-cos2α)/(1+cos2α)
(1-cos2α)/(1+cos2α)=(1-1+2sin²α)/(1+2cos²α-1)
=2sin²α/2cos²α
=tan²α

Answer 2

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