# Question #cd107

Jan 31, 2015

Let's first draw a triangle to get the trigonometry right.

We'll use $\angle A$ instead of $x$ because of the picture

$\cos A$ is defined as $b / h$
$\tan A$ is defined as $a / b$

So we get: $\cos A \cdot \tan A = \frac{\cancel{b}}{h} \cdot \frac{a}{\cancel{b}} = \frac{a}{h}$

Which is the definition of the sine .

$\cos A \cdot \tan A = \sin A$

Extra
You could have done this another way if you knew that

$\tan A = \sin \frac{A}{\cos} A$

Then it would be:

$\cos A \cdot \tan A = \cancel{\cos A} \cdot \sin \frac{A}{\cancel{\cos A}} = \sin A$ (same result)

(picture: Wikipedia)

Nov 7, 2017

$\cos x \tan x \equiv \sin x$

#### Explanation:

$\cos x \tan x \equiv \cos x \cdot \sin \frac{x}{\cos} x \equiv \sin x$