/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 Verify the identity. $$\frac{\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 38

Verify the identity. $$\frac{\tan x+\tan y}{1-\tan x \tan y}=\frac{\cot x+\cot y}{\cot x \cot y-1}$$

Short Answer

Expert verified
The given trigonometric identity has been verified correctly.

Step by step solution

01

Expressing tangents in terms of cotangents

Remember that \( \tan x = \frac{1}{\cot x} \) and \( \tan y = \frac{1}{\cot y} \). Substitute these into the left side of the identity. The expression will be: \( \frac{\frac{1}{\cot x} + \frac{1}{\cot y}}{1-\frac{1}{\cot x \cot y}} \)
02

Simplify the left side

Make the denominators on the left side the same by multiplying each term by \( \cot x \cot y \): \[ \frac{\cot y + \cot x}{\cot x \cot y - 1} \]which simplifies to the right side of the given identity.
03

Conclusion

Because both sides of the equation can be rewritten to \( \frac{\cot y + \cot x}{\cot x \cot y - 1} \), it's proof that the given trigonometric identity holds true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

True or False? In Exercises \(81-84\) , determine whether the statement is true or false. Justify your answer. \(\sin \left(x-\frac{\pi}{2}\right)=-\cos x\)

Evaluating Functions lnvolving Double Angles In Exercises \(21-24\) , find the exact values of \(\sin 2 u, \cos 2 u\) and tan 2\(u\) using the double-angle formulas. $$\sin u=-3 / 5, \quad 3 \pi / 2

Using a Double-Angle Formula In Exercises \(15-20\) , use a double-angle formula to rewrite the expression. $$10 \sin ^{2} x-5$$

Using Half-Angle Formulas, use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. $$75^{\circ}$$

Using Sum-to-Product Formulas. use the sum-to-product formulas to rewrite the sum or difference as a product. $$ \sin 5 \theta-\sin 3 \theta $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.