Skip Navigation

Simplifying Trigonometric Expressions

Convert to sine/cosine and use basic trig identities to simplify.

Atoms Practice
Estimated10 minsto complete
Practice Simplifying Trigonometric Expressions
This indicates how strong in your memory this concept is
Estimated10 minsto complete
Practice Now
Turn In
Simplifying Trigonometric Expressions

How could you write the trigonometric function more simply?

Simplifying Trigonometric Expressions

Now that you are more familiar with trig identities, we can use them to simplify expressions. Remember, that you can use any of the following identities.

Reciprocal Identities: and

Tangent and Cotangent Identities: and

Pythagorean Identities: and

Cofunction Identities: and

Negative Angle Identities: and

Let's simplify the following expressions.

When simplifying trigonometric expressions, one approach is to change everything into sine or cosine. First, we can change secant to cosine using the Reciprocal Identity.

Now, combine the denominator into one fraction by multiplying 1 by .

Change this problem into a division problem and simplify.

With this problem, we need to factor the numerator and denominator and see if anything cancels. The rules of factoring a quadratic and the special quadratic formulas can be used in this scenario.

In the last step, we simplified to the left hand side of the Pythagorean Identity. Therefore, this expression simplifies to 1.

First, pull out the GCF.

Now, from the Pythagorean Identities, so simplify further.


Example 1

Earlier, you were asked to simplify the trigonometric function .

Notice that the terms in the expression have a common factor of , so start by factoring this common term out.

Now, use the trigonometric identity , substitute, and simplify.

Simplify the following trigonometric expressions.

Example 2

Use the Cotangent Identity and the Cofunction Identity .

Example 3

Use the Negative Angle Identity and the Tangent Identity.

Example 4

In this problem, you will use several identities.


Simplify the following expressions.

Answers for Review Problems

To see the Review answers, open this PDF file and look for section 14.8. 

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Simplifying Trigonometric Expressions.
Please wait...
Please wait...