Question

If cos2x + sinx = √2 cosx, prove that : cosx - sinx = +-√2 sinx

Answer 1

helllo..

$given$

$\cos(x) + \sin(x) = \sqrt{2} \cos(x)$

$then( \sqrt{2} - 1) \cos(x) = \sin(x)$

$on \: multiplying \: bothside \: by( \sqrt{2} + 1)$

$we \: get( \sqrt{2 + 1} ( \sqrt{2 - 1} \cos \: x = ( {2 + 1}) \sin(x)$

$\cos(x) = \sqrt{2} \sin(x ) + \sin(x)$

$=> \cos(x) - \sin(x) = \sqrt{2} \sin(x)$

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