Question

Find the general solution of $\sqrt{3}\cos x+\sin x=2$

Answer 1

given, $\sqrt{3}\cos x+\sin x=2$

$\frac{\sqrt{3}}{2}\cos x+\frac{1}{2}\sin x=1$

$\cos \frac{\pi }{6}\cos x+\sin \frac{\pi }{6}\sin x=1$

$\cos (\frac{\pi }{6}-x)=1$

$\Rightarrow \frac{\pi }{6}-x=2n\pi$

$\Rightarrow -x=2n\pi -\frac{\pi }{6}$

$\therefore x=\frac{\pi }{6}-2n\pi$