Question

how do you get from tan(theta) + cot(theta) to equal sec(theta) csc(theta)

Answer 1

Substitute tanx=sinx/cosx and cotx=cosx/sinx. Add the fractions by finding like denominators and simplify.

Answer 2

You will also need to use the Pythagorean identity for sinx and cosx.

Answer 3

\[\tan \theta+\cot \theta \]\[\frac{ \sin \theta }{ \cos \theta } + \frac{ \cos \theta }{ \sin \theta } \]\[\frac{ \sin ^{2}\theta }{ \cos \theta \sin \theta }+\frac{ \cos ^{2}\theta}{\cos \theta \sin \theta}\]\[\frac{ 1 }{ \sin \theta \cos \theta }\]\[\frac{ 1 }{ \sin \theta }\frac{ 1 }{ \cos \theta }\]\[\csc \theta \sec \theta\]