Q. 43 Establish each identitysin聽2胃+... [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. 43 (page 504)

Establish each identity
$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \tan (3 胃)$

Short Answer

Expert verified

The derivation of the equation $\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \tan (3 胃)$ is

$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \frac{2 \sin (\frac{2 胃 + 4 胃}{2}) \cos (\frac{2 胃 + 4 胃}{2})}{2 \cos (\frac{2 胃 + 4 胃}{2}) \cos (\frac{2 胃 + 4 胃}{2})} = \frac{\sin (3 胃)}{\cos (3 胃)} = \tan (3 胃)$

Step by step solution

Step 1. Given data

The given equation for derivation is

$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \tan (3 胃)$

Step 2. Derivation

Take left-hand side expression and use sum-to-product formula

$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \frac{2 \sin (\frac{2 胃 + 4 胃}{2}) \cos (\frac{2 胃 + 4 胃}{2})}{2 \cos (\frac{2 胃 + 4 胃}{2}) \cos (\frac{2 胃 + 4 胃}{2})} = \frac{2 \sin (3 胃) \cos (3 胃)}{2 \cos (3 胃) \cos (3 胃)} = \frac{\sin (3 胃)}{\cos (3 胃)} = \tan (3 胃)$

The left-hand side expression is equal to the right-hand side expression

So identity is stabilised

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91影视

Establish each identity
$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \tan (3 胃)$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Derivation

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91影视

Establish each identitysin2胃+sin4胃cos2胃+cos4胃=tan(3胃)

Short Answer

Step by step solution

Step 1. Given data

Step 2. Derivation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Mechanics Maths

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Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Establish each identity
$\frac{\sin (2 胃) + \sin (4 胃)}{\cos (2 胃) + \cos (4 胃)} = \tan (3 胃)$