The general solution of x - x = 2 , for any integer n is - Vidyadip

MCQ

The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is

A
$n\pi $
✓
$2n\pi + \frac{{3\pi }}{4}$
C
$2n\pi $
D
$(2n + 1)\,\pi $

✓

Answer

Correct option: B.

$2n\pi + \frac{{3\pi }}{4}$

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

$\Rightarrow \cos \left( {x + \frac{\pi }{4}} \right) = - 1$

==> $x + \frac{\pi }{4} = 2n\pi \pm \pi $

$\Rightarrow 2n\pi + \frac{{3\pi }}{4}{\rm{\,\,or\,\,}}\,\,2n\pi - \frac{{5\pi }}{4}$ .

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