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Exercises Trigonometry

Example 9 from Algebra and Trigonometry, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions

Rewriting a Trigonometric Expression Using the Difference of Squares

Rewrite the trigonometric expression using the difference of squares: $4 \cos^{2} θ - 1.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
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.
$\begin{matrix} 4 \cos^{2} θ - 1 & = & {(2 \cos θ)}^{2} - 1 \\ = & (2 \cos θ - 1) (2 \cos θ + 1) \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Rewrite the trigonometric expression using the difference of squares: $25 - 9 \sin^{2} θ .$

How did it go?

PreviousWriting the Trigonometric Expression as an Algebraic Expression Next Simplify by Rewriting and Using Substitution

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 9.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.