If cosA + sinA= root2 cosA, show that cosA - sinA=root2 sinA

1.	If cosA + sinA= root2 cosA, show that cosA - sinA=root2 sinA
Answer» In given take cosA to rhs take common, and then whatever you will get take, it to lhs again now rationalize the denominator and solve yu will get the proof............? CosA +sinA =\xa0√2cosAsquaring⇒(cosA + sin A)² = (√2cosA)²⇒cos²A + sin²A\xa0+ 2sinAcosA = 2cos²A⇒1\xa0-\xa0sin²A\xa0+ 1 -\xa0cos²A\xa0+ 2sinAcosA\xa0= 2cos²A⇒2 - 2cos²A =\xa0cos²A + sin²A -\xa02sinAcosA\xa0⇒2(1 - cos²A)= (cosA - sinA)²⇒\xa0cosA - sinA =\xa0√[2sin²A]⇒cosA-sinA =\xa0√2sinA

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