This post is part of the HSC Maths Extension 1 syllabus, under the topic Further Trignometry focusing on t-formula.

The t-formulae are the following:

if we let:

t = tan( \frac{x}{2}Then we can express:

sin(x) = \frac{2t}{1+t^2} cos(x) = \frac{1-t^2}{1+t^2} tan(x) = \frac{2t}{1-t^2}To learn more about how we derive the t-formulae, let’s start with an explanation of the t formulae (PART 1)

### Explanation of the t formula

Now that we understand they are derived, let’s look at all the identities.

### Identities from the t formulae

Finally, let’s understand how to also prove identities.