14-1 Trigonometric Identities

Objective

To verify trigonometric identities

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You may recognize x 2 = 5 x − 6 x squared , equals 5 x minus 6 as an equation that you are to solve to find the few, if any, values of x that make the equation true. On the other hand, you may recognize x 5 x 3 = x 2 , fraction x to the fifth , over x cubed end fraction . equals , x squared . comma as an identity, an equation that is true for all values of x for which the expressions in the equation are defined. (Here, x 5 x 3 fraction x to the fifth , over x cubed end fraction is not defined for x = 0 . ) x equals 0 . close

A trigonometric identity in one variable is a trigonometric equation that is true for all values of the variable for which all expressions in the equation are defined.

Essential Understanding The interrelationships among the six basic trigonometric functions make it possible to write trigonometric expressions in various equivalent forms, some of which can be significantly easier to work with than others in mathematical applications.

Some trigonometric identities are definitions or follow immediately from definitions.

The domain of validity of an identity is the set of values of the variable for which all expressions in the equation are defined.

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