How do I solve $6csc^2x=cotx+8$ if $o<x<360$ ?

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Answer 1 · 2018-05-15T10:44:08

See below

$6csc^2x=cotx+8$

Using $csc^2x= 1+cot^2x$ :
$6(1+cot^2x)=cotx+8$

$6cot^2x-cotx-2=0$

$6cot^2-4cotx+3cotx-2=0$

$3cotx(2cotx+1)-2(2cotx+1)=0$

$cotx=2/3$
Which is essentially:
$tanx= 3/2$

$x=arctan(3/2)approx 56.31^@+180^@= 236.31^@$
$x= 56.31^@, 236.31^@$

$cotx= -1/2$
Which is essentially:
$tanx=-2$

$x= 296.57^@, 116.57^@$

How do I solve 6csc^2x=cotx+86csc^2x=cotx+8 if o<x<360o<x<360?