Rewriting a trigonometric expression using the difference of squares
Rewrite the trigonometric expression:
Notice that both the coefficient and the trigonometric expression in the first term are squared, and the square of the number 1 is 1. This is the difference of squares. Thus,
There are multiple ways to represent a trigonometric expression. Verifying the identities illustrates how expressions can be rewritten to simplify a problem.
Graphing both sides of an identity will verify it. See
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Simplifying one side of the equation to equal the other side is another method for verifying an identity. See
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The approach to verifying an identity depends on the nature of the identity. It is often useful to begin on the more complex side of the equation. See
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We can create an identity by simplifying an expression and then verifying it. See
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Verifying an identity may involve algebra with the fundamental identities. See
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Algebraic techniques can be used to simplify trigonometric expressions. We use algebraic techniques throughout this text, as they consist of the fundamental rules of mathematics. See
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Section exercises
Verbal
We know
is an even function, and
and
are odd functions. What about
and
Are they even, odd, or neither? Why?
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