Question

Find general solution of $Cosecx=-2$ ?

Answer 1

$\csc x=-2$

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

$\Rightarrow \sin x=\sin (\pi +\frac{\pi }{6})=\sin \frac{7\pi }{6}$ $(\because \sin \frac{7\pi }{6}=-\frac{1}{2})$

The general solution of an equation of the type

$\sin x=\sin y$

is $x=n\pi +(-1{)}^{n}y$; $n\in Integers$

$\therefore$ General solution of the equation

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

$\Rightarrow x=n\pi +(-1{)}^n\frac{7\pi }{6}$ ; $n\in Integers$