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^@#