SinA+CosA is equal to root2.cosa then prove that sinA-cosA is equal to

1.	SinA+CosA is equal to root2.cosa then prove that sinA-cosA is equal to root2.sinA
Answer» sinA+cosA=root2.cosAS.B.S.(sinA+cosA)^2=root 2 sq.cos^2Asin^2A+cos^2A+2sinA.cosA=2.cos^2A1+2sinA.cosA=2.cos^2A---(sin^2A+cos^2A=1)2sinA.cosA=2cos^2A-1L.H.S.sinA-cosAS.B.S.(sinA-cosA)^2=sin^2A+cos^2A-2sinA.cosA=1-2sinA.cosA (sin^2A+cos^2A=1)=1-(2cos^2A-1) (2sinA.cosA=2cos^2A-1)=1-2cos^2A+1=2-2cos^2A=2(1-cos^2A)=2.sin^2A(SinA-cosA)^2=2.sin^2AsinA-cosA=root2.sin^2A (whole root)sinA-cosA=root2.sinA

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