Q. 66 In Problems ,47-68聽establish ea... [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. 66 (page 496)

In Problems , $47 - 68$ establish each identity.
$\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$

Short Answer

Expert verified

The identity $\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$ is established.

Step by step solution

Step 1 Given identity is,

$\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$

The formulae used in this problem are,

$\tan (2 胃) = \frac{2 \tan 胃}{1 - \tan^{2} 胃} \tan (3 胃) = \frac{(3 \tan 胃 - \tan^{3} 胃)}{1 - 3 \tan^{2} 胃} \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$

Step 2 Use the formula in the required places and prove that the values of the expressions in both the sides are equal.

$\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = \tan 胃 + \frac{\tan 胃 + \tan 120^{掳}}{1 - \tan 胃 \tan 120^{掳}} + \frac{\tan 胃 + \tan 240^{掳}}{1 - \tan 胃 \tan 240^{掳}} = \tan 胃 + \frac{\tan 胃 - \sqrt{3}}{1 + \sqrt{3} \tan 胃} + \frac{\tan 胃 + \sqrt{3}}{1 - \sqrt{3} \tan 胃} = \frac{(\tan 胃 - 3 \tan^{3} 胃) + 8 \tan 胃}{1 - 3 \tan^{2} 胃} = \frac{3 (3 \tan 胃 - \tan^{3} 胃)}{1 - 3 \tan^{2} 胃} \tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$

Hence, proved.

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91影视

In Problems , $47 - 68$ establish each identity.
$\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$

Short Answer

Step by step solution

Step 1 Given identity is,

Step 2 Use the formula in the required places and prove that the values of the expressions in both the sides are equal.

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91影视

In Problems ,47-68establish each identity.tan胃+tan胃+120掳+tan胃+240掳=3tan3胃

Short Answer

Step by step solution

Step 1 Given identity is,

Step 2 Use the formula in the required places and prove that the values of the expressions in both the sides are equal.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In Problems , $47 - 68$ establish each identity.
$\tan 胃 + \tan (胃 + 120^{掳}) + \tan (胃 + 240^{掳}) = 3 \tan (3 胃)$