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Exercises Trigonometry

Example 3 from Algebra and Trigonometry, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions

Verifying the Equivalency Using the Even-Odd Identities

Verify the following equivalency using the even-odd identities:

(1 + \sin x) [1 + \sin (- x)] = \cos^{2} x

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
Working on the left side of the equation, we have

$\begin{matrix} (1 + \sin x) [1 + \sin (- x)] & = & (1 + \sin x) (1 - \sin x) & Since sin(− x)= - \sin x \\ = & 1 - \sin^{2} x & Difference of squares \\ = & \cos^{2} x & {cos}^{2} x = 1 - \sin^{2} x \end{matrix}$

How did it go?

PreviousVerifying a Trigonometric Identity Next Verifying a Trigonometric Identity Involving sec2θ

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.