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Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 9.1 Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions

Verifying a Trigonometric Identity

Verify $\tan θ \cos θ = \sin θ .$

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
We will start on the left side, as it is the more complicated side:

$\begin{matrix} \tan θ \cos θ & = & (\frac{\sin θ}{\cos θ}) \cos θ \\ = & (\frac{\sin θ}{\cos θ}) \cos θ \\ = & \sin θ \end{matrix}$

Your turn

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

Verify the identity $\csc θ \cos θ \tan θ = 1.$

How did it go?

PreviousGraphing the Equations of an Identity Next Verifying the Equivalency Using the Even-Odd Identities

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.