(Ä°) If cose-sine-12sin9, then prove that cose+sine-/2cose – InterviewSolution

1.	(Ä°) If cose-sine-12sin9, then prove that cose+sine-/2cose
Answer» CosA +sinA =√2cosAsquaring⇒(cosA + sin A)² = (√2cosA)²⇒cos²A + sin²A+ 2sinAcosA = 2cos²A⇒1-sin²A+ 1 -cos²A+ 2sinAcosA= 2cos²A⇒2 - 2cos²A =cos²A + sin²A -2sinAcosA⇒2(1 - cos²A)= (cosA - sinA)²⇒cosA - sinA =√[2sin²A]⇒cosA-sinA =√2sinAhence proved

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