/*! 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 24 Verify the identity. $$\frac{\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 24

Verify the identity. $$\frac{\sec \theta-1}{1-\cos \theta}=\sec \theta$$

Short Answer

Expert verified
Therefore, the given identity is verified.

Step by step solution

01

Transform to sine and cosine

Let's first transform the secant function to cosine. This will give us: \[\frac{1}{\cos \theta}-1\] for the numerator of the left hand side of the equation.
02

Simplify the numerators

Next, let's find a common denominator to simplify the numerators. This means we will have \[\frac{1-\cos \theta}{\cos \theta}\] as the numerator on the left hand side.
03

Simplify the fraction

The numerator and the denominator of the left hand side both have a \(1-\cos \theta\) term, so they cancel each other out. Leaving us with \[\frac{1}{\cos \theta}\] which is equal to our right hand side: \[\sec \theta\]

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

Consider the equation \(2 \sin x-1=0\). Explain the similarities and differences between finding all solutions in the interval \(\left[0, \frac{\pi}{2}\right)\), finding all solutions in the interval \([0,2 \pi),\) and finding the general solution.

Find the exact value of the expression. $$\cos 120^{\circ} \cos 30^{\circ}+\sin 120^{\circ} \sin 30^{\circ}$$

Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval \([0,2 \pi)\). $$\frac{1+\sin x}{\cos x}+\frac{\cos x}{1+\sin x}=4$$

(a) use a graphing utility to graph the function and approximate the maximum and minimum points on the graph in the interval \([0,2 \pi),\) and (b) solve the trigonometric equation and demonstrate that its solutions are the \(x\) -coordinates of the maximum and minimum points of \(f .\) (Calculus is required to find the trigonometric equation.) Function $$f(x)=\sin ^{2} x+\cos x$$ Trigonometric Equation $$2 \sin x \cos x-\sin x=0$$

Fill in the blank. \(\sin (u+v)=\)_____
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

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.