Question

Verify the identity tan x + cot x =csc x× sec x

Answer 1

Tan(x) + cot(x) can be expressed as the following:

$\frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)}$

Find the common denominator:

$\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}$

We can use a Pythagorean identity to replace $sin^2(x) + cos^2(x)$ with 1.

So now we have $\frac{1}{sin(x)cos(x)}$ or $\frac{1}{sin(x)} * \frac{1}{cos(x)}$

Which equals:

$csc(x)sec(x)$