Derivative

mathemagician1729 · Yang-Mills Theory Offline Joined: 07 Jun 2008 Posts: 544

Find the tangent line of $y = 4 + \cot x -2\csc x$
at $x = \frac{\pi}{2}$

I would like an elegant solution.

**Posted:** Sun Nov 01, 2009 6:49 pm

akech

Rewrite the given formula as $f(x) = 4 + \frac {\cos x - 2}{\sin x}$

We have $f'(x) = - \left(\frac {1 - 2\cos x}{\sin^2 x}\right)$

We have $f(\frac {\pi}{2}) = 2$ and $f'(\frac {\pi}{2}) = - 1$ so that the line that you want is given as follows:

$y - 2 = - 1(x - \frac {\pi}{2}) \implies y = - x + 2 + \frac {\pi}{2}$

**Posted:** Sun Nov 01, 2009 8:39 pm

AndrewTom

Alternative solution:

**Posted:** Sun Nov 01, 2009 11:56 pm