Question

If cos A+sin A=root 2cos (90-A) show that sin A-cos A=root 2 cos A

Answer 1

cosA+sinA=√2cos(90-A)
or, cosA+sinA=√2sinA
or,cosA=√2sinA-sinA
or,cosA=sinA(√2-1)
or,cosA=sinA{(√2-1)(√2+1)/(√2+1)}
or,cosA=sinA{(2-1)/(√2+1)}
or,cosA=sinA/(√2+1)
or,√2cosA+cosA=sinA
or,cosA-sinA=-√2cosA
or,sinA-cosA=√2cosA