How do you verify the identity secx-cos^2xcscx=tanxsecx?

Nov 22, 2016

This equation is not correct if you pick a value for x say $\frac{\pi}{3}$and plug it in to both sides then you can see that it is not a true statement.

Nov 22, 2016

The equation is not true.

Explanation:

Check if the equation is true or not by computing the left side, then the right side:

Left Side:
$\sec x - {\cos}^{2} x \csc x$
$= \frac{1}{\cos} x - {\cos}^{2} \frac{x}{\sin} x$
$= \frac{\sin x - {\cos}^{2} x \cos x}{\cos x \sin x}$
$= \frac{\sin x - {\cos}^{3} x}{\cos x \sin x}$

Right Side:
$\tan x \sec x$
$= \sin \frac{x}{\cos} x \cdot \frac{1}{\cos} x$
$= \sin \frac{x}{\cos} ^ 2 x$

The equation above is not true because the left side of the equation is not equal to the right side of the equation:
$\frac{\sin x - {\cos}^{3} x}{\cos x \sin x} \cancel{=} \sin \frac{x}{\cos} ^ 2 x$