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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)