Evaluate an indefinite integral (Trig)

Question

∫ (cosθ/sin²θ) dθ

How would you evaluate this function? I saw a substitution method but I wasn't taught that in my class so I don't think I want to be using that way, unless it's the only way. The answer was -1/sinθ+C.

Answer 1

Here is a way that bypasses the "substitution" method:

Let "theta" = T

You can rewrite the integral as integral [cosT/sinT)(1/sinT)dT

= integral (cotT)(cscT)dt

= -cscT + C = -1/(sinT) + C