Question

Simplify each expression. $\frac{\sin \theta \csc \theta}{\cot \theta}$

   Simplify each expression. 
$\frac{\sin \theta \csc \theta}{\cot \theta}$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 14, Problem 25

Instant Answer

Solved by Expert Joshua Eastwood

04/07/2020

Step 1

So, the expression becomes $\frac{\sin \theta \cdot \frac{1}{\sin \theta}}{\cot \theta}$. Show more…

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Simplify each expression. $\frac{\sin \theta \csc \theta}{\cot \theta}$

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Key Concepts

Quotient Identities

Quotient identities relate the tangent and cotangent functions to sine and cosine. In particular, cot ? is defined as cos ?/sin ?. Using this identity is key in simplifying expressions involving cotangent, as it allows rewriting the expression in terms of sine and cosine.

Simplification of Trigonometric Expressions

Simplification of trigonometric expressions involves applying identities and algebraic techniques to rewrite an expression in a simpler or more useful form. In problems like these, substituting equivalent forms and canceling common factors help in reducing the expression to a simpler trigonometric function.

Reciprocal Identities

Reciprocal identities are fundamental relationships in trigonometry that express a trigonometric function as the reciprocal of another. For example, recognizing that csc ? is the reciprocal of sin ? (csc ? = 1/sin ?) allows for the substitution that simplifies the expression.

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