When we add or subtract angles, the result is called a compound angle. For example, is a compound angle. Using a calculator, we find:

This shows that is not equal to . Instead, we can use the following identities:

• Addition formulae are given in a condensed form:

These formulae are used to expand trigonometric functions to help us simplify or evaluate trigonometric expressions of this form.

See how we approach this two-part question:

Question

1. By writing determine the exact value of

2. Find the exact value of

1.

Using the formula for

Using exact values that you should know:

2. Since then:

Using the formula for

Using exact values that you should know: