/*! 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 57 Use the fundamental identities t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 57

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\cot u \sin u+\tan u \cos u$$

Short Answer

Expert verified
The simplified form of the expression \( \cot u \sin u + \tan u \cos u \) is \(\cos(u) + \sin(u)\)

Step by step solution

01

Substitute the expressions

The first step is to substitute the trigonometric functions with their equivalents in sine and cosine. Here, subtitute \(\cot(u)\) as \(\frac{1}{\tan(u)}\), which can be rewritten as \(\frac{\cos(u)}{\sin(u)}\), and \(\tan(u)\) as \(\frac{\sin(u)}{\cos(u)}\). Therefore, the initial expression can be written as \((\frac{\cos(u)}{\sin(u)} \sin(u)) + (\frac{\sin(u)}{\cos(u)} \cos(u))\)
02

Simplify the expression

Now simplify each term of the expression. Since the \(\sin(u)\) in the denominator of the first term cancels out with the \(\sin(u)\) in the numerator, and the \(\cos(u)\) in the denominator of the second term cancels out with the \(\cos(u)\) in the numerator, the expression simplifies to \(\cos(u) + \sin(u)\)
03

Final answer

Once the expression is simplified, we have the final answer. The expression \( \cot u \sin u + \tan u \cos u \) simplifies to \(\cos(u) + \sin(u)\)

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

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\frac{\cos x \cot x}{1-\sin x}=3$$

Write the expression as the sine, cosine, or tangent of an angle. $$w\sin 3 \cos 1.2-\cos 3 \sin 1.2$$

Write the expression as the sine, cosine, or tangent of an angle. $$\cos 130^{\circ} \cos 40^{\circ}-\sin 130^{\circ} \sin 40^{\circ}$$

Find the exact values of the sine, cosine, and tangent of the angle. $$-\frac{7 \pi}{12}$$

Solve the multiple-angle equation. $$\sin \frac{x}{2}=-\frac{\sqrt{3}}{2}$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.