若cos2a/cos(a+π/4)=√2,则cosa+sina的值为?

若cos2a/cos(a+π/4)=√2,则cosa+sina的值为?
若cos2a/cos(a+π/4)=√2,则cosa+sina的值为?

若cos2a/cos(a+π/4)=√2,则cosa+sina的值为?
cos2a/cos(a+π/4)=√2
(cos²a-sin²a)/(cosacosπ/4-sinasinπ/4)=√2
(cos²a-sin²a)/(cosa-sina)=√2×(√2/2)
(cosa-sina)(cosa+sina)/(cosa-sina)=1
cosa+sina=1