cos/(1+tan)-sin/(1+cot)化简
网友回答
cos/(1+tan)-sin/(1+cot)
=cos/(1+sin/cos)-sin/(1+cos/sin)
=cos^2/(cos+sin)-sin^2(sin+cos)
=(cos^2-sin^2)/(sin+cos)
=cos-sin
=√2cos(a+π/4)
======以下答案可供参考======
供参考答案1:
cos/(1+tan)-sin/(1+cot)
=cos/(1+sin/cos)-sin/(1+cos/sin)
=cos^2/(cos+sin)-sin^2(sin+cos)
=(cos^2-sin^2)/(sin+cos)
=cos-sin
=√2cos(a+π/4)