Question

(cot^-1)(cosecx + cotx)
differentiate w.r.t x

Answer 1

try u sub
\[u=\text{csch}(\cot (x))\text{ and }v=\text{}[\cot^{-1} (x)]\]

Answer 2

\[cosec x + \cot x = \frac{1+ \cos x}{sinx}\]
\[ = \frac{2\cos^2(x/2)}{2\sin(x/2)\cos(x/2)}\]
=cot (x/2)

Therefore,
Now you can try :)

Answer 3

@rroat

Answer 4

A plot of the problem expression is attached.