证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}

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证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}

证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}
证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}

证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}
用逆推法
证明:2/(tanα-cotα)=sin2α/{(2sin^2)α-1}
2/(sina/cosa-cosa/sina)=2sinacosa/(-cos2a)
1/[(sin²a-cos²a)/(sinacosa)]=sinacosa/(-cos2a)
sinacosa/(-cos2a)=sinacosa/(-cos2a)
恒成立
以上各步可逆
证毕
注意:cos²a-sin²a=1-2sin²a=cos2a