Solve the equation #|cotx|=|cotx+1/sinx|#?

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Answer 1 · 2018-01-13T09:41:08

#x=2npi+-(2pi)/3#

As #|cotx|=|cotx+1/sinx|=|cotx+cscx|#

#cot^2x=cot^2x+csc^2x+2cotxcscx#

or #csc^2x+2cotxcscx=0#

or #cscx(cscx+2cotx)=0#

But we cannot have #cscx=0#, hence

#cscx+2cotx=0# and multiplying by #sinx# (if it is not zero)

#2cosx=-1# or #cosx=-1/2=cos((2pi)/3)#

#x=2npi+-(2pi)/3#