True-or-False :If $cosec x=1+\cot x$ then $x=2n\pi,2n\pi+\large\frac{\pi}{2}$

Question

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

Answer 1

$cosec x=1+\cot x$

Squaring both sides

$cosec^2 x=(1+\cot x)^2$

$1+\cot ^2x=1+\cot^2x+2\cot x$

$cosec^2x=\cot^2x+1$

$2\cot x=0$

$\cot x=0$

$\therefore x=(2n+1)\large\frac{\pi}{2}$

Hence the given statement is true.