HSC Together Year 12 Maths Extension 1: Further Trigonometry: t-formulae

#### Maths Extension 1

• Proof
• Vectors
• Further Trigonometric Functions
• Further Calculus
• Further Statistical Analysis
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# Further Trigonometry: t-formulae

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}

### 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.

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