二倍角与半角的正弦、余弦和正切的题~1+cosa-sina 1-cosa-sina

网友回答

(1+cos(a)-sin(a))/(1-cos(a)-sin(a))+(1-cos(a)-sin(a))/(1+cos(a)-sin(a))
首先通分,公分母为:
(1-sin(a))^2-(cos(a))^2=1-2*sin(a)+(sin(a))^2-(cos(a))^2=2*(sin(a))^2-2*sin(a)=2*sin(a)*(sin(a)-1)
第一项分子为:
(1+cos(a)-sin(a))*(1+cos(a)-sin(a))=2-2*sin(a)+2*cos(a)-2*sin(a)*cos(a)
第二项分子为:
(1-cos(a)-sin(a))*(1-cos(a)-sin(a))=2-2*sin(a)-2*cos(a)+2*sin(a)*cos(a)
两项相加为:
4-4*sin(a)=-4*(sin(a)-1)
再除以分母为:
-2/(sin(a))
即最终化简结果.
======以下答案可供参考======
供参考答案1:
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