Q. 11 聽Establish the identitycsc胃+co... [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. 11 (page 505)

Establish the identity
$\frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}$

Short Answer

Expert verified

Rationalizing the numerator and denominator by multiply numerator and denominator by

$c s c 胃 - c o t 胃 a n d s e c 胃 - \tan 胃 w e g e t \frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}$

Step by step solution

Step 1. Given information

\frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}

Step 2. Rationalizing the numerator and denominator

$W e h a v e g i v e n, \frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃} T a k e L H S \frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃}$

Rationalizing the numerator and denominator by multiply numerator and denominator by $c s c 胃 - c o t 胃 a n d s e c 胃 - \tan 胃$

$(\frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃}) (\frac{c s c 胃 - c o t 胃}{c s c 胃 - c o t 胃}) (\frac{s e c 胃 - \tan 胃}{s e c 胃 - \tan 胃}) = \frac{(c s c^{2} 胃 - c o t^{2} 胃) (s e c 胃 - \tan 胃)}{(s e c^{2} 胃 - \tan^{2} 胃) (c s c 胃 - c o t 胃)} a s c s c^{2} 胃 - c o t^{2} 胃 = 1 s e c^{2} 胃 - \tan^{2} 胃 = 1 = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}$

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91影视

Establish the identity
$\frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rationalizing the numerator and denominator

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91影视

Establish the identitycsc胃+cot胃sec胃+tan胃=sec胃-tan胃csc胃-cot胃

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rationalizing the numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Applied Mathematics

Probability and Statistics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Establish the identity
$\frac{c s c 胃 + c o t 胃}{s e c 胃 + \tan 胃} = \frac{s e c 胃 - \tan 胃}{c s c 胃 - c o t 胃}$