Trigonometric Identities - Simplify Expressions
In these lessons, we will learn to use trigonometric identities to simplify trigonometric expressions. These video lessons with examples, step-by-step solutions, and explanations help High School Algebra 2 students learn to use trigonometric identities to simplify trigonometric expressions.
Related Pages
Trigonometric Graphs
Lessons On Trigonometry
Trigonometric Functions
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.
Example:
Simplify \(\frac{{\sin \theta \sec \theta }}{{{{\cos }^2}\theta }}\)
Solution:
\(\frac{{\sin \theta \sec \theta }}{{{{\cos }^2}\theta }} = \frac{{\sin \theta \sec \theta }}{{\cos \theta \cos \theta }}\)
\(= \tan \theta \cdot \frac{{\sec \theta }}{{\cos \theta }}\)
= tan θ • sec2 θ
= tan θ (tan2 θ + 1)
= tan3 θ + tan θ
Example:
Simplify \(\frac{{{{\sin }^2}\theta }}{{\cos \theta }} + \frac{{{{\cos }^2}\theta }}{{\cos \theta }}\)
Solution:
\(\frac{{{{\sin }^2}\theta }}{{\cos \theta }} + \frac{{{{\cos }^2}\theta }}{{\cos \theta }}\)
\(= \frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{\cos \theta }}\)
\(= \frac{1}{{\cos \theta }}\)
= sec θ
Simplifying Trigonometric Expressions Using Identities
Example:
(tan3x)(csc3x)
How to Simplify Trigonometric Expressions Using Identities?
Example:
sec x cos x − cos2 x
(csc2 x − 1)(sec2 x sin2 x)
Using Identities to Simplify Trigonometric Expressions
Example:
(csc2 x − 1)/csc2 x
(csc2 x − cot2 x)/(tan2 x - sec2 x)
Algebraic Manipulation of Trigonometric Functions
Distributive Property, FOIL, Factoring.
Example:
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
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