cos2a/sin(a-π/4)=-√2/2
(cos²a-sin²a)/(sinacosπ/4-cosasinπ/4)=-√2/2
∴[(cosa+sina)(cosa-sina)]/[√2/2(sina-cosa)]=-√2/2
∴-√2 (cosa+sina)=-√2/2
∴sina+cosa=1/2
cos2a/sin(a-π/4)=-√2/2
(cos²a-sin²a)/(sinacosπ/4-cosasinπ/4)=-√2/2
∴[(cosa+sina)(cosa-sina)]/[√2/2(sina-cosa)]=-√2/2
∴-√2 (cosa+sina)=-√2/2
∴sina+cosa=1/2