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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#