Since the cotangent function is defined as
[tex] \cot(x) = \dfrac{\cos(x)}{\sin(x)} [/tex]
we have that the cotangent equals zero at [tex] \frac{\pi}{2} [/tex], because we have
[tex] \cot\left(\dfrac{\pi}{2}\right) = \dfrac{\cos\left(\frac{\pi}{2}\right)}{\sin\left(\frac{\pi}{2}\right)} = \dfrac{0}{1} =0 [/tex]
So, the limit simply becomes
[tex] \dfrac{\pi}{2}\cdot 0 = 0 [/tex]
