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Answer 1 · 2018-02-01T09:24:20

$x=pi/6, (5pi)/6 or (3pi)/2$

The equation can be rearranged to get:
$csc^2x-cscx-2=0$

Let's make $a=cscx$

$a^2-a-2=0$

$(a+1)(a-2)=0$

$a=-1 or a=2$

Therefore $cscx=-1 or 2$

$cscx=1/sinx$

$sinx=-1/1 or 1/2$

$sinx=-1 or 1/2$

$x=sin^(-1)(-1)=(3pi)/2$

or

$x=sin^(-1)(1/2)=pi/6 or (pi-pi/6)=(5pi)/6$

So, $x=pi/6, (5pi)/6 or (3pi)/2$