Answer
$t+csc(t)+C$
Work Step by Step
Given: $\int(1-csc(t) cot(t))dt$
Integrate:
Integral of $1$ is $t$
Integral of $-csc(t)cot(t)$ is $csc(t)+C$
So $\int(1-csc(t) cot(t))dt=t+csc(t)+C$
Check the result by differentiation:
$\frac{d}{dt}(t+csc(t)+C)=1-csc(t)cot(t)$
