Q. 109 If tan聽伪=x+1and role="math" lo... [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. 109 (page 487)

If $\tan 伪 = x + 1$ and role="math" localid="1646425111199" $\tan 尾 = x - 1,$ show that
role="math" localid="1646426027733" $2 c o t (伪 - b) = x^{2}$

Short Answer

Expert verified

The equation $2 c o t (伪 - b) = x^{2}$ can be obtained by multiplying equations $\tan 伪 = x + 1 & \tan 尾 = x - 1$

$(\tan 伪) (\tan 尾) = (x + 1) (x - 1) (\tan 伪) (\tan 尾) + 1 = x^{2} 2 \frac{(\tan 伪) (\tan 尾) + 1}{\tan 伪 - \tan 尾} = x^{2} 2 c o t (伪 - 尾) = x^{2}$

Step by step solution

Step 1. Given data

Given equations are

$\tan 伪 = x + 1 鈰� (i) \tan 尾 = x - 1 鈰� (i i)$

Given equation that needs to be proven is

$2 c o t (伪 - b) = x^{2}$

Step 2. Addition of equations

Subtract equation ii from the equation i

$\tan 伪 - \tan 尾 = (x + 1) - (x - 1) \tan 伪 - \tan 尾 = x + 1 - x + 1 \tan 伪 - \tan 尾 = 2 \frac{\tan 伪 - \tan 尾}{2} = 1 鈰� (i i i)$

Step 3. multiplication of equations

Multiply equations i and ii

$(\tan 伪) (\tan 尾) = (x + 1) (x - 1) (\tan 伪) (\tan 尾) = x^{2} - 1 (\tan 伪) (\tan 尾) + 1 = x^{2} \frac{(\tan 伪) (\tan 尾) + 1}{1} = x^{2} 鈰� (i v)$

Step 4. Proof

Use Equation iii in equation iv

$\frac{(\tan 伪) (\tan 尾) + 1}{1} = x^{2} \frac{(\tan 伪) (\tan 尾) + 1}{\frac{\tan 伪 - \tan 尾}{2}} = x^{2} \frac{2}{\frac{\tan 伪 - \tan 尾}{(\tan 伪) (\tan 尾) + 1}} = x^{2} \frac{2}{\tan (伪 - 尾)} = x^{2} 2 c o t (伪 - 尾) = x^{2}$

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91影视

If $\tan 伪 = x + 1$ and role="math" localid="1646425111199" $\tan 尾 = x - 1,$ show that
role="math" localid="1646426027733" $2 c o t (伪 - b) = x^{2}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Addition of equations

Step 3. multiplication of equations

Step 4. Proof

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91影视

If tan伪=x+1and role="math" localid="1646425111199" tan尾=x-1,show thatrole="math" localid="1646426027733" 2cot(伪-b)=x2

Short Answer

Step by step solution

Step 1. Given data

Step 2. Addition of equations

Step 3. multiplication of equations

Step 4. Proof

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Applied Mathematics

Geometry

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

If $\tan 伪 = x + 1$ and role="math" localid="1646425111199" $\tan 尾 = x - 1,$ show that
role="math" localid="1646426027733" $2 c o t (伪 - b) = x^{2}$