化简cosa*根号下(1-sina/1+sina)+sina*根号下(1-cosa/1+cosa)
人气:116 ℃ 时间:2019-09-20 06:15:42
解答
条件不足
设a是第四象限角,化简cosa根号下(1-sina)/(1+sina)+sina根号下(1-cosa)/(1+cosa)
cosa√(1-sina)/(1+sina)+sina√(1-cosa)/(1+cosa)
=cosa*|sina/2-cosa/2|/|sina/2+cosa/2|+sina*|sina/2|/|cosa/2|
∵a是第四象限角
∴sina/2+cosa/2<0,sina/2-cosa/2>0,sina/2与cosa/2异号
∴原式=-(cosa/2+sina/2)(cosa/2-sina/2)*(sina/2-cosa/2)/(sina/2+cosa/2)-2sina/2*cosa/2*(sina/2)/(cosa/2)
=(cosa/2-sina/2)^2-2(sina/2)^2
=1-sina-(1-cosa)
=-sina+cosa
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