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Answer 1 · 2017-12-04T14:56:19

$x=1.571,3.309,6.116$

$csc^2x+5cscx-6=0$ can be factorized as under

$csc^2x+6cscx-cscx-6=0$

or $cscx(cscx+6)-1(cscx+6)=0$

or $(cscx-1)(cscx+6)=0$

i.e. either $cscx-1=0$ i.e. $cscx=1$ and $x=pi/2=1.571$

or $cscx+6=0$

i.e. $cscx=-6$ i.e. $x=6.116$ or $3.309$ (in radians)