Question

Verify that each equation is an identity by using any of the identities introduced in the first three sections of this chapter. $$\frac{\cot s-\tan s}{\cos s+\sin s}=\frac{\cos s-\sin s}{\sin s \cos s}$$

Name: Problem 105, Chapter 10: A Graphical Approach to Precalculus with Limits
Uploaded: 2020-08-20T02:04:46-08:00
Duration: 2 min 51 s
Channel: Amy Jiang
Description: Verify that each equation is an identity by using any of the identities introduced in the first three sections of this chapter. (cots-tans)/(coss+sins)=(coss-sins)/(sins coss)

   Verify that each equation is an identity by using any of the identities introduced in the first three sections of this chapter.
$$\frac{\cot s-\tan s}{\cos s+\sin s}=\frac{\cos s-\sin s}{\sin s \cos s}$$

A Graphical Approach to Precalculus with Limits

John Hornsby,… 7th Edition

Chapter 10, Problem 105

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Solved by Expert Amy Jiang

08/20/2020

Step 1

We can split the fraction into two fractions as follows: $$\frac{\cos s-\sin s}{\sin s \cos s} = \frac{\cos s}{\sin s \cos s} - \frac{\sin s}{\sin s \cos s}$$ Show more…

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Verify that each equation is an identity by using any of the identities introduced in the first three sections of this chapter. $$\frac{\cot s-\tan s}{\cos s+\sin s}=\frac{\cos s-\sin s}{\sin s \cos s}$$

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Key Concepts

Algebraic Manipulation Techniques

Algebraic manipulation techniques, including factoring, combining like terms, and finding common denominators, are crucial when working with trigonometric expressions. These techniques help transform complex expressions into simpler forms, making it possible to verify that two expressions are equivalent identities.

Trigonometric Identities

Trigonometric identities are equations that establish relationships between trigonometric functions and are true for all values of the variable where the functions are defined. They serve as essential tools for simplifying expressions and proving equivalences in trigonometry.

Quotient and Reciprocal Identities

Quotient and reciprocal identities relate trigonometric functions such as tangent and cotangent to sine and cosine. These identities enable the conversion of one trigonometric function into another, facilitating easier manipulation and simplification of expressions.

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