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

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 00:17:00

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

(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)

前面分子用平方差公式打开，分母化成用正余弦表示。后面的1用sin^22x+cos^22x表示，平方和，分母用正余弦表示 约分就出来了。

已知tan=2,求(cos x+sin x)/(cos x-sin x)+sin^2x 化简(sin x+cos x-1)(sin x-cos x+1)/sin 2x 2cos x (sin x -cos x)+1 y=2cos x (sin x+cos x) 化简sin(x)cos(x)cos(2x) 化简sin(x)cos(x)cos(2x) sin x cos x cos 2x 化简 (sin^2x+cos^2x )(sin^2x-cos^2x)怎么得sin^2x-cos^2x? 化简 cos^2(x)*sin^2(x)-sin^2(x) 化简 cos^(2)(x)*sin^(2)(x)-sin^(2)(x) 已知sin(x)+3cos(x)=2,求sin(x)-cos(x)/sin(x)+cos(x)=? 化简sin^4x-sin^2x+cos^2x 化简:sin^4 x-sin^2 x+cos^2 x sin(x/2)cos(x/2)= 化简sin^4x+cos^2x sin[cos^2(x^3+x)],求导 y=(sin x + COS x)^2 化简(sin^2x-cos^4x+cos^2x-sin^4x)/(sin^2x-cos^6x+cos^2x-sin^6x)