OML Search

Trigonometric Identities - Simplify Expressions

Related Topics: More Trigonometric Identities


In these lessons, we will learn how to use trigonometric identities to simplify trigonometric expressions.

The following are some common trigonometric identities: Reciprocal Identities, Quotient Identities and Pythagorean Identities. Scroll down the page for examples and solutions using the identities to simply trigonometric expressions.

Trig Identities


Simplify \(\frac{{\sin \theta \sec \theta }}{{{{\cos }^2}\theta }}\)


\(\begin{array}{c}\frac{{\sin \theta \sec \theta }}{{{{\cos }^2}\theta }} = \frac{{\sin \theta \sec \theta }}{{\cos \theta \cos \theta }}\\ = \tan \theta \cdot \frac{{\sec \theta }}{{\cos \theta }}\\ = \tan \theta \cdot {\sec ^2}\theta \\ = \tan \theta ({\tan ^2}\theta + 1)\\ = {\tan ^3}\theta + \tan \theta \end{array}\)


Simplify \(\frac{{{{\sin }^2}\theta }}{{\cos \theta }} + \frac{{{{\cos }^2}\theta }}{{\cos \theta }}\)


\(\begin{array}{c}\frac{{{{\sin }^2}\theta }}{{\cos \theta }} + \frac{{{{\cos }^2}\theta }}{{\cos \theta }} = \frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{\cos \theta }}\\ = \frac{1}{{\cos \theta }}\\ = \sec \theta \end{array}\)

Simplifying Trigonometric Expressions Using Identities
(tan3x)(csc3x) How to Simplify Trigonometric Expressions Using Identities?
sec x cos x − cos2 x
(csc2 x − 1)(sec2 x sin2 x) Using Identities to Simplify Trigonometric Expressions
(csc2 x − 1)/csc2 x
(csc2 x − cot2 x)/(tan2 x - sec2 x) Algebraic Manipulation of Trigonometric Functions
Distributive Property, FOIL, Factoring.
cos y(tan y - sec y)
(sin x + cos x)(sin x - cos x)
sin2x cos2x + cos4x

Algebraic Manipulation of Trigonometric Functions with fractions
Simplifying Complex Fractions, Multiplying, Dividing, Adding and Subtracting Fractions. Algebraic Manipulation of Trigonometric Functions - Radical Expressions
Multiplying, Dividing, Simplifying. Rationalizing the Denominator. Algebraic Manipulation of Trigonometric Functions - Complex Examples

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines