若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?知道的请写步骤~其中a为角度
问题描述：
若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?
知道的请写步骤~其中a为角度
答
cos2a/sin(a-π/4)=-√2/2
√2(cosa-sina)(cosa+sina)/(sina-cosa)=-√2/2
cosa+sina=1/2
答
cos2a/sin(a-π/4)
=(cos²a-sin²a)/[(√2/2)(sina-cosa)]
=(cosa+sina)(cosa-sina)/[(√2/2)(sina-cosa)]
=-(cosa+sina)/(√2/2)
=-√2/2
所以
cosa+sina=1/2
答
cos2a/sin(a-π/4)=(2cos2a*cos(a-π/4)) /(2sin(a-π/4) cos(a-π/4)) cos2a/sin(a-π/4)=(2cos2a*cos(a-π/4)) /sin(2a-π/2) cos2a/sin(a-π/4)=-(2cos2a*cos(a-π/4)) /cos2a cos2a/sin(a-π/4)=-2*cos(a-π/4) ...