# How do you prove tanx + cotx = secx cscx?

Nov 28, 2015

#### Explanation:

Given:
$\tan x + \cot x = \sec x \cdot \csc x$

Start on the right hand side, change it to $\sin x$ ; $\cos x$

$\sin \frac{x}{\cos} x + \cos \frac{x}{\sin} x = \sec x \cdot \csc x$

$\textcolor{red}{\left[\sin \frac{x}{\sin} x\right]} \cdot \left(\sin \frac{x}{\cos} x\right)$ + color(blue) [cosx/cosx]*cosx/sinx = $\sec x \cdot \csc x$

$\frac{{\sin}^{2} x + {\cos}^{2} x}{\sin x \cdot \cos x} = \sec x \cdot \csc x$

$\frac{1}{\sin x \cdot \cos x} = \sec x \cdot \csc x$

$\left(\frac{1}{\sin} x\right) \left(\frac{1}{\cos} x\right) = \sec x \cdot \csc x$

$\sec x \cdot \csc x = \sec x \cdot \csc x$

Prove completed!

*${\sin}^{2} x + {\cos}^{2} x = 1$

*$\frac{1}{\sin} x = \csc x$ ; $\frac{1}{\cos} x = \sec x$