Q. The general solution of $\sin{x - \cos{x = \sqrt{2}}}$, for any integer $n$ is
A) $n\pi$
B) $2n\pi + \frac{3\pi}{4}$
C) $2n\pi$
D) $(2n + 1)\pi$
Explanation
(b)
Given, $\frac{1}{\sqrt{2}}\sin{x - \frac{1}{\sqrt{2}}\cos{x = 1}}$
$\Rightarrow \ \cos\left( x + \frac{\pi}{4} \right) = - 1$
$\Rightarrow \ \ x + \frac{\pi}{4} = 2n\pi + \pi\ \ \Rightarrow \ \ \ x = 2n\pi + \frac{3\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.