若cos(2A)/sin(A-(pi/4))=-(√2)/2,则cosA+sinA等于多少?

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若cos(2A)/sin(A-(pi/4))=-(√2)/2,则cosA+sinA等于多少?
若cos(2A)/sin(A-(pi/4))=-(√2)/2,则cosA+sinA等于多少?

若cos(2A)/sin(A-(pi/4))=-(√2)/2,则cosA+sinA等于多少?
cos(2A)/sin(A-(pi/4))=-(√2)/2
=>cosA^2-sinA^2=-(√2)/2*[sinAcos(-pi/4)+cosAsin(-pi/4)]
=>(cosA+sinA)(cosA-sinA)=-(√2)/2*[(√2)/2*sinA-(√2)/2*cosA]
=>(cosA+sinA)(cosA-sinA)=1/2(cosA-sinA)
=>cosA+sinA=1/2