Fundamental Identities

Let us study about fundamental identities,
If an equation contains one or more variables and is valid for all replacement values of the variables for which both sides of the equation are defined, then the equation is known as an identity. The equation x2 + 2 x = x( x + 2), for example, is an identity because it is valid for all replacement values of x.

If an equation is valid only for certain replacement values of the variable, then it is called a conditional equation. The equation 3 x + 4 = 25, for example, is a conditional equation because it is not valid for all replacement values of x. An equation that is said to be an identity without stating any restrictions is, in reality, an identity only for those replacement values for which both sides of the identity are defined. For example, the identity
is valid only for those values of α for which both sides of the equation are defined.

The fundamental (basic) trigonometric identities can be divided into several groups. First are the reciprocal identities.
Hope the above explanation helped you.