Using Trigonometric Identities


Back to Integration Topics Page


Recall of Trigonometric Identities

You need to remember the trignometric identities that you have learnt throughout the A Level Course to integrate expressions with terms that can not be integrated by replacing these terms with equivalent terms/expressions that can be integrated. Below are all of the identities you will have covered in the syllabus:

The * formulas are formulas that do not appear in the formula booklet, but are extremely important to memorise for any question involving Trigonometry, including Integration ones. But even if the other formulas appear in the formulae booklet, you need to still get used to using them frequently, as you never know what cases you will get in the exam, and you will need to try to apply any of these formulas instantly.

Example 1:

Example 1
Answer 1
Example 2
Answer 2

Example 2:

Example 1
Answer 1
Example 2
Answer 2

Practice Question:

Example 1
Example 2

Answer 2

Note: It is common to see a question like this where in the first part, you have to do some sort of algebraic manipulation using the trig identities to prove an algebraic expression and the second part involves using your answer from the first part to integrate the expression given. If you are unable to prove the first part, do not spend too long on it, as almost all the time the part you need for the second part will be given to you.