/*! 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 75 Explain how to verify an identit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 75

Explain how to verify an identity.

Short Answer

Expert verified
To verify an identity, choose either the more complex side or any side if both are equally complex, simplify the side using known identities and basic operations, and then compare with the other side to confirm if the identity is verified.

Step by step solution

01

Understand the Problem

An identity is an equation that is true for all values of the variable in its domain. Verify means to prove or check whether it is true. However, remember that you can perform operations on both sides independently to make them look identical.
02

Start On One Side

Choose the more complicated side of the equation. If both sides are equally complex, choose either side. Make this side, your 'working-side' from now on.
03

Use Known Identities

Use the appropriate identities in order to simplify the working side of the equation. You may replace sin^2 x with 1 - cos^2 x or cos^2 x with 1 - sin^2 x. Similarly if you have a tan x = sin x/cos x, sin^2 x + cos^2 x = 1 and many more.
04

Simplify The Equation

Simplify the working side as much as possible using responses from elementary operations such as addition, subtraction, multiplication and division. Break up fractions or combine fractions as needed.
05

Compare With Other Side

After simplification, the working side should be the same as the non-working side. If both the sides are not identical, check the work. If they look identical, the identity is verified.

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

Solve each equation on the interval \([0,2 \pi)\) Do not use a calculator. $$ \sin 3 x+\sin x+\cos x=0 $$

A hot-air balloon is rising vertically. From a point on level ground 120 feet from the point directly under the passenger compartment, the angle of elevation to the balloon changes from \(37.1^{\circ}\) to \(62.4^{\circ} .\) How far, to the nearest tenth of a foot, does the balloon rise during this period?

Find the exact value of each expression. Do not use a calculator. $$ \sin \left[\sin ^{-1} \frac{3}{5}-\cos ^{-1}\left(-\frac{4}{5}\right)\right] $$

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$ 2 \cos 2 x+1=0 $$

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$ 5 \sin x=2 \cos ^{2} x-4 $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.