Question

Define an identity.

Answer 1

An identity is an equation which is true for all values of the variable (s).

For example,

 `(x+3)^2=x^2+6x+9`

Any number of variables may involve in an identity.

An example of an identity containing two variables is

 `(x+y)^2=x^2+2xy+y^2`

The above are all about algebraic identities. Now, we define the trigonometric identities.

An equation involving trigonometric ratios of an angle 0 (say) is said to be a trigonometric identity if it is satisfied for all valued of 0 for which the trigonometric ratios are defined.

For examples,

\[\sin^2 \theta + \cos^2 \theta = 1\]
\[1 + \tan^2 \theta = \sec^2 \theta\]
\[1 + \cot^2 \theta = {cosec}^2 \theta\]