Q. 16 Establish the identity 聽聽聽ta... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 16 (page 505)

Establish the identity
$\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$

Short Answer

Expert verified

By converting tan and cot functions into sin and cos we get $\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$

Step by step solution

Step 1. Given information

$\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$

Step 2. Rewriting the given expression

Take LHS, $\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃}$

$\frac{\frac{\sin 胃}{\cos 胃} - \frac{\cos 胃}{\sin 胃}}{\frac{\sin 胃}{\cos 胃} + \frac{\cos 胃}{\sin 胃}} = \frac{\sin^{2} 胃 - \cos^{2} 胃}{\sin^{2} 胃 + \cos^{2} 胃} A s \sin^{2} 胃 + \cos^{2} 胃 = 1 \frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = \sin^{2} 胃 - \cos^{2} 胃$

Step 3. Calculations

Now,

$\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = \sin^{2} 胃 - \cos^{2} 胃 \frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - \cos^{2} 胃 - \cos^{2} 1 = 1 - 2 \cos^{2} 胃 A s \sin^{2} 胃 + \cos^{2} 胃 = 1 \sin^{2} 胃 = 1 - \cos^{2} 胃 \frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$

LHS=RHS

Hence identity is established.

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91影视

Establish the identity
$\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewriting the given expression

Step 3. Calculations

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91影视

Establish the identity tan胃-cot胃tan胃+cot胃=1-2cos2胃

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rewriting the given expression

Step 3. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Decision Maths

Statistics

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Establish the identity
$\frac{\tan 胃 - c o t 胃}{\tan 胃 + c o t 胃} = 1 - 2 \cos^{2} 胃$