How do you simplify #\frac { \tan \theta + \cot \theta } { \tan \theta } #?

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Answer 1 · 2017-07-05T02:06:32

#(tantheta + cottheta)/(tantheta) = color(blue)(csc^2theta#

This expression can also be written as

#(tantheta)/(tantheta) + (cottheta)/(tantheta)#

#1 + (cottheta)/(tantheta)#

#1 + cot^2theta#

We can use the trigonometric identity

#1 + cot^2theta = csc^2theta#

The simplified version is thus #color(blue)(csc^2theta#.