Question

Simplify each expression. $\csc \theta \tan \theta+\sec \theta$

   Simplify each expression.
$\csc \theta \tan \theta+\sec \theta$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 14, Problem 54

Instant Answer

Solved by Expert Elizabeth Xu

04/29/2020

Step 1

We know that $\csc \theta$ is $1/\sin \theta$ and $\tan \theta$ is $\sin \theta/\cos \theta$. So, the expression becomes: \[ \frac{1}{\sin \theta} \cdot \frac{\sin \theta}{\cos \theta} + \sec \theta \] Show more…

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Simplify each expression. $\csc \theta \tan \theta+\sec \theta$

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Key Concepts

Reciprocal Identities

Reciprocal identities are key in trigonometry, defining functions such as cosecant, secant, and cotangent in terms of sine, cosine, and tangent. They establish that csc ? is the reciprocal of sin ? and sec ? is the reciprocal of cos ?, which simplifies transformation and manipulation in expressions.

Expressing Functions in Terms of Sine and Cosine

Writing trigonometric functions using sine and cosine is a standard method for simplifying and manipulating trigonometric expressions. This approach leverages the relationships among the basic trigonometric functions and facilitates common operations, such as combining terms under a common denominator.

Simplification of Trigonometric Expressions

Simplifying trigonometric expressions involves rewriting and reducing expressions by exploiting identities and common factors. Techniques include substituting equivalent definitions, finding common denominators, and canceling common factors to obtain a simpler or more convenient form.

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