Question

证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}

证明2/(tanα-cotα)=sin2α/{(2sin^2)α-1}

Answer 1

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