(cos^2 2x-sin^2 2x)/(1-tan2x)=(1+2sin2xcos2x)/(1+tan2x)

问题描述:

(cos^2 2x-sin^2 2x)/(1-tan2x)=(1+2sin2xcos2x)/(1+tan2x)

(1+2sin2xcos2x)/(cos²2x-sin²2x)
= (sin²2x+cos²2x+2sin2xcos2x)/(cos²2x-sin²2x)
= (sin2x+cos2x)²/[(cos2x+sin2x)(cos2x-sin2x)]
= (sin2x+cos2x)/(cos2x-sin2x)
= (1+tan2x)/(1-tan2x)【分子分母同除cos2x】
移项得:(cos^2 2x-sin^2 2x)/(1-tan2x)=(1+2sin2xcos2x)/(1+tan2x)