Chapter 7: Q. 4 (page 495)

True or False
$\tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$

Short Answer

Expert verified

Equation $\tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$ is true

Step by step solution

Step 1. Given Data

The given equation is

$\tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$

Step 2. Explanation

Use sum formula for $\tan (α + β)$

role="math" localid="1646429460524" $\tan (α + β) = \frac{\tan α + \tan β}{1 - (\tan α) (\tan β)}$

Substitute $θ$ forrole="math" localid="1646429474469" $β & α$

$\tan (θ + θ) = \frac{\tan θ + \tan θ}{1 - (\tan θ) (\tan θ)} \tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$

so the given equation is true

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True or False
$\tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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True or Falsetan2θ=2tanθ1-tan2θ

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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Most popular questions from this chapter

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True or False
$\tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ}$