Can you solve tantheta - cottheta = 0 over [0, 2pi) ?

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Answer 1 · 2018-03-31T04:10:44

#theta=pi/4, (3pi)/4, (5pi)/4, (7pi)/4#

#tantheta-cottheta=0#

#tantheta=cottheta#

Recall that the cotangent is simply the reciprocal of the tangent.

#tantheta=1/tantheta#

Cross-multiply:

#tan^2theta=1#

Taking the root of both sides yields

#tantheta=+-1#

Now, consider where the tangent function is equal to positive or negative one over #[0, 2pi).# This holds true for

#theta=pi/4, (3pi)/4, (5pi)/4, (7pi)/4#