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Question
Define an identity.
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Solution
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,
\[\sin^2 \theta + \cos^2 \theta = 1\]
\[1 + \tan^2 \theta = \sec^2 \theta\]
\[1 + \cot^2 \theta = {cosec}^2 \theta\]
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