Expressing sin(x) and cos(x) in terms of tan(x)

In this tutorial, we are going to write sinx and cosx in terms of tanx, because these are going to be some trigonometric identities that can help us later on, especially when we come to integrating
trigonometric functions.

Imagine a right angle triangle with a hypotenuse of 1 and a horizontal side of length a, and a vertical side of length b, and the acute angle between a and the hypotenuse as x.

So in this instance, sinx = b; cosx = a; and tanx = b/a

By Pythagoras' Theorem, we have the sides a² + b² = 1, and thus cos²x + sin²x = 1 (the Pythagorean Identity)

So if we divide this identity by cos²x...

Which equates to...

And if we flip this over, we'll get...

And thus...

Please watch the video for the full tutorial!