若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是

问题描述:

若((cos2a)/(sin(a+(π/4))))=-√2/2则cosa-sina的值是

由cos2α/sin(α-π/4)=-(√2)/2,且cos2α=cos²α-sin²αsin(α-π/4)=(√2)/2*(sinα-cosα)则:cos2α/sin(α-π/4)=cos²α-sin²α/((√2)/2*(sinα-cosα))=-(√2)/2等式左边同时约去sinα-co...