How do you find the exact value of #tan2theta=cottheta# in the interval #0<=theta<360#?

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Answer 1 · 2016-12-25T17:16:29

#theta=30^@# or #150^@# or #180^@# or #330^@#

#tan2theta=cottheta#

#hArr(2tantheta)/(1-tan^2theta)=1/tantheta#

or #2tan^2theta=1-tan^2theta#

or #3tan^2theta-1=0#

or #(sqrt3tantheta+1)(sqrt3tantheta-1)=0#

i.e. #tantheta=1/sqrt3# or #-1/sqrt3#

and general solution is #theta=npi+-pi/6#

and in the interval #0<=theta<360^@#

#theta=30^@# or #150^@# or #180^@# or #330^@#