Cot θ +(1/cot θ)

Question

How would I perform the indicated operation and simplify the result so that there are no quotients?

Answer 1

The expression is cot θ +(1/cot θ)

=(cot θ/1) +(1/cot θ)

= (cot²θ + 1)/cot θ

Recall the formula: cot²θ + 1 = cosec² θ

= (cosec²θ)/cot θ

=(1 / sinθ)²/(cos θ/sinθ)

=1/sinθcos θ

=2/2sinθcos θ

=2/sin2θ

=2cosec 2θ