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Question

If sinA+cosA=2cosA then the value of cos A - sin A = ?

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Solution

sinA+cosA=2cosA
sin2A+cos2A+2sinAcosA=2cos2A2sinAcosA=2cos2A1=cos2A=cos2Asin2A2sinAcosA=(cosA+sinA)(cosAsinA)cosAsinA=2sinAcosAcosA+sinA=2sinAcosA2cosAcosAsinA=2sinA

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