Identity- An equation that is always true
Ex: 2x+5 = 2(x-3) + 11 <---- No matter what you put in for X the sides will always be equal
Identities are used for substitution
Reciprocal Identities:
Quotient Identities:
Pythagorean Identities:
Pythagorean Identities can be derived from other equations. Such as-
Using those two factors we can derive the first pythagorean identity by using the pythagoean theorem and finding a new identity that we can use to substitute.
Plug in the factors
distribute the square 
factor out a c^2
divide by c^2 to get the first Pythagorean identity The other two identities can be derived in a similar way. The three Pythagorean identities are:
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