若cos2α/sin(α+7/4×π)=-√2/2,则cosα+sinα的值
问题描述：
若cos2α/sin(α+7/4×π)=-√2/2,则cosα+sinα的值
答
cos2α/sin(α+7/4*π)
=cos2α/sin(α+2*π - π/4)
=cos2α/sin(α-π/4)
=cos2α/[sinα*cos(π/4) - cosα*sin(π/4)]
=[(cosα)^2 - (sinα)^2]/[√2/2*(cosα - sinα)]
=√2*(cosα + sinα) = -√2/2
所以,
cosα + sinα = -1/2