Question

simplify tan(theta)+cot(theta)

Answer 1

looks simple to me like that
but you can try
\[\frac{b}{a}+\frac{a}{b}\] and see if you get something nice

Answer 2

when you add those you get
\[\frac{b^2+a^2}{ab}\] and since \(\sin^2(x)+\cos^2(x)=1\) that is the same as
\[\frac{1}{\sin(x)\cos(x)}\] but i don't see why that is "simpler" in any way