An identity is an equation that is true for all values of the variable. Some basic identities are:

To prove that an identity is true: change either side, or both sides, until the sides are the same.

Example 1

csc =

I would work with the right side. Try to get it to look like the left side. Change cot to sin and cosine s.

You have now proved the identity!

Example 2

sec - sec sin² = cos

I would work with the left side. Factor out a sec .

sec (1 - sin² ) = cos

Since sin² + cos² = 1,
cos² = 1 - sin²

So, sec (cos² ) = cos

Example 3