Question

Find the general solution of cosec x = -2.

Answer 1

Given,

$cosecx=-2$

$\sin x=-\frac{1}{2}$

Let $\sin x=\sin y$

$⟹\sin y=-\frac{1}{2}$

$\sin y=\sin \frac{7\pi }{6}$

$y=\frac{7\pi }{6}$

Since, $\sin x=\sin y$

General solution is :

$x=n\pi +(-1{)}^n\frac{7\pi }{6},n\in Z$