Q. 77 Establish each identity.聽(secv-... [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. 77 (page 475)

Establish each identity.
$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$

Short Answer

Expert verified

The left side of the given equation has been simplified to bring the right side.

Step by step solution

Step 1. Given Information

The given equation is $\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$

Step 2. Calculation

Consider the left side of the given equation and simplify to bring the right side in order to establish the equation.

$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = \frac{{(\frac{1}{\cos v} - \frac{\sin v}{\cos v})}^{2} + 1}{\frac{1}{\sin v} (\frac{1}{\cos v} - \frac{\sin v}{\cos v})} = \frac{\frac{{(1 - \sin v)}^{2}}{\cos^{2} v} + 1}{\frac{1}{\sin v} (\frac{1 - \sin v}{\cos v})} = \frac{\frac{{(1 - \sin v)}^{2} + \cos^{2} v}{\cos^{2} v}}{\frac{1 - \sin v}{\sin v \cos v}} = \frac{1 + \sin^{2} v + \cos^{2} v - 2 \sin v}{\cos v} 脳 \frac{\sin v}{1 - \sin v} = \frac{2 - 2 \sin v}{1 - \sin v} 脳 \frac{\sin v}{\cos v} = \frac{2 (1 - \sin v)}{1 - \sin v} 脳 \tan v = 2 \tan v$

Hence, Proved.

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91影视

Establish each identity.
$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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91影视

Establish each identity.(secv-tanv)2+1cscv(secv-tanv)=2tanv

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Logic and Functions

Statistics

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Establish each identity.
$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$