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

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

$cosec x=1+\cot x$
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.