若cos2x/sin(x-派/4)=-√2/2,则cosx+sinx的值为?

问题描述:

若cos2x/sin(x-派/4)=-√2/2,则cosx+sinx的值为?

(cos²x-sin²x)/(sinxcosπ/4-cosxsinπ/4)=-√2/2
(cosx+sinx)(cosx-sinx)/[-√2/2(cosx-sinx)]=-√2/2
所以cosx+sinx=1/2