已知cos(π-2α)/sin(α-(π/4)) =-负二分之根号二 求sinα+cosα=

网友回答

cos(π-2α)/sin(α-(π/4)) = -√2/2
2cos2α =√2sin(α-(π/4))
=√2(sinαcosα(π/4)-cosαsin(π/4))
= sinα-cosα
2((cosα)^2-(sinα)^2 = sinα-cosα
2(cosα+sinα)(cosα-sinα)= sinα-cosα
sinα+cosα = -1/2
======以下答案可供参考======
供参考答案1:
用a代替cos2a/(sinacosπ/4-cosasinπ/4)=-√2/2
(cos²a-sin²a)/(sinacosπ/4-cosasinπ/4)=-√2/2
(cosa+sina)(cosa-sina)/[-√2/2*(cosa-sina)]=-√2/2
所以cosa+sina=1/2