Q. 64 In problems 19-98, establish eac... [FREE SOLUTION]

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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 64 (page 474)

In problems 19-98, establish each identity.
$\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u) = 1$

Short Answer

Expert verified

We have proved the identity $\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u) = 1$ .

Step by step solution

Step 1. Given information.

We have:

$\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u) = 1$

Step 2. Establish the identity.

Take the left hand side:

$\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u)$

$= \frac{\frac{\sin (u)}{\cos (u)} - \frac{\cos (u)}{\sin (u)}}{\frac{\sin (u)}{\cos (u)} + \frac{\cos (u)}{\sin (u)}} + 2 \cos^{2} (u) = \frac{\frac{\sin^{2} (u) - \cos^{2} (u)}{\cos (u) \sin (u)}}{\frac{\sin^{2} (u) + \cos^{2} (u)}{\cos (u) \sin (u)}} + 2 \cos^{2} (u) = \frac{\sin^{2} (u) - \cos^{2} (u)}{\cos (u) \sin (u)} 脳 \frac{\cos (u) \sin (u)}{\sin^{2} (u) + \cos^{2} (u)} + 2 \cos^{2} (u) = \frac{\sin^{2} (u) - \cos^{2} (u)}{1} + 2 \cos^{2} (u) = \sin^{2} (u) - \cos^{2} (u) + 2 \cos^{2} (u) = \sin^{2} (u) + \cos^{2} (u) = 1$

Hence, proved.

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91影视

In problems 19-98, establish each identity.
$\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u) = 1$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

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91影视

In problems 19-98, establish each identity.tanu-cotutanu+cotu+2cos2u=1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In problems 19-98, establish each identity.
$\frac{\tan (u) - \cot (u)}{\tan (u) + \cot (u)} + 2 \cos^{2} (u) = 1$