若cos2a/sin(a-π/4)=-根号2/2 则sina+cosa 的值为多少?用高中知识回答

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