How to solve #cosxtanx+tanx=cosx+1# if #0<x<360#?

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Answer 1 · 2018-05-15T10:21:17

See below

#cosxtanx+tanx=cosx+1#

#cosxtanx+tanx-cosx= 1#

#cosxtanx+tanx-cosx=1#

#cosxtanx+tanx-cosx-1=0#

Factor by grouping
#tanx(cosx+1)-1(cosx+1)=0#

#tanx=1#
#x= 45^@, 225^@#
#x=pi/4+pin#

#cosx=-1#
#x=180^@#
#x=pi+2pin#