Answer
$$\int^{3\pi/4}_{\pi/4}\csc z\cot zdz=0$$
Work Step by Step
$$A=\int^{3\pi/4}_{\pi/4}\csc z\cot zdz$$ $$A=-\csc z\Big]^{3\pi/4}_{\pi/4}=-\frac{1}{\sin z}\Big]^{3\pi/4}_{\pi/4}$$ $$A=-\Big(\frac{1}{\sin(3\pi/4)}-\frac{1}{\sin(\pi/4)}\Big)$$ $$A=-\Big(\frac{1}{\frac{\sqrt2}{2}}-\frac{1}{\frac{\sqrt2}{2}}\Big)$$ $$A=0$$
