Question

What is this limit equal to?

Answer 1

Since the cotangent function is defined as

$\cot(x) = \dfrac{\cos(x)}{\sin(x)}$

we have that the cotangent equals zero at $\frac{\pi}{2}$, because we have

$\cot\left(\dfrac{\pi}{2}\right) = \dfrac{\cos\left(\frac{\pi}{2}\right)}{\sin\left(\frac{\pi}{2}\right)} = \dfrac{0}{1} =0$

So, the limit simply becomes

$\dfrac{\pi}{2}\cdot 0 = 0$