if cosA + sinA = square root of 2 multiplied by cosA, then show that cosA - sinA = square root of 2 multiplied by sinA

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Solution

CosA+SinA=root2CosA

SinA=root2CosA-CosA

SinA=CosA(root2-1)

Multiply by (root2+1) on numerator as well as denominator

SinA=CosA(root2-1)(root2+1) / (root2+1)
SinA=CosA(2-1) / (root2+1)
SinA=CosA / (root2+1)
CosA=SinA(root2+1)
CosA=root2SinA+SinA
CosA-SinA=root2SinA
Thus Proved

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