Trigonometric Identities (Edexcel IGCSE Further Pure Maths)
Revision Note
Written by: Roger B
Reviewed by: Dan Finlay
Trigonometric Identities
What is a trigonometric identity?
Trigonometric identities are statements about trigonometric functions like , and
They are true for all values of the angle
They can be used to help simplify trigonometric equations before solving them
Sometimes you may see identities written with the symbol instead of an equals sign
This means 'identical to' or 'equivalent to'
What trigonometric identities do I need to know?
You must know these two trigonometric identities:
This is the identity for
This is sometimes called the Pythagorean identity
Note that the notation is the same thing as
The second identity is often used in one of its rearranged forms
Examiner Tips and Tricks
When asked to show that one thing is equal or identical to another, look at what parts are 'missing'
This can help you spot which identity to use
Worked Example
Show that the equation can be written in the form , where , and are integers to be found with .
Note that in the 'target' form there is no or
That means we want to use a substitution to get rid of the in the original form
We can do this using the identity , rearranged as
Substitute that back into the original equation
Multiply both sides of the equation by to make the coefficient positive
This gets the equation into the required form with , and
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