If n is any integer, then the general solutio | vedclass

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Question

(c) Given equation is,$\cos x - \sin x = \frac{1}{{\sqrt 2 }}$

Dividing equation by $\sqrt 2 $,

$\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2

Vedclass · Accepted Answer

$x = 2n\pi + \frac{\pi }{{12}}$ or $x = 2n\pi - \frac{{7\pi }}{{12}}$

Vedclass · Answer

(c) Given equation is,$\cos x - \sin x = \frac{1}{{\sqrt 2 }}$

Dividing equation by $\sqrt 2 $,

$\frac{1}{{\sqrt 2 }}\cos x - \frac{1}{{\sqrt 2 }}\sin x = \frac{1}{2}$

$\cos \left( {\frac{\pi }{4} + x} \right) = \cos \frac{\pi }{3}$.

Hence, $\frac{\pi }{4} + x = 2n\pi \pm \frac{\pi }{3}$

$x = 2n\pi + \frac{\pi }{3} - \frac{\pi }{4} = 2n\pi + \frac{\pi }{{12}}$

or $x = 2n\pi - \frac{\pi }{3} - \frac{\pi }{4} = 2n\pi - \frac{{7\pi }}{{12}}$.

If $n$ is any integer, then the general solution of the equation $\cos x - \sin x = \frac{1}{{\sqrt 2 }}$ is

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