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Chapter 7: Q. 6 (page 495)

True or False:
$\tan 2 θ + \tan 2 θ = \tan (4 θ)$

Short Answer

Expert verified

The given statement/expression is false.

Step by step solution

01

Step 1. Given information

The given function is $\tan (2 θ) + \tan (2 θ) = \tan (4 θ)$

02

Step 2. True or False

From double angle formula,

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

So,

$\tan 2 θ + \tan 2 θ \frac{2 \tan θ}{1 - \tan^{2} θ} + \frac{2 \tan θ}{1 - \tan^{2} θ} \frac{4 \tan θ}{1 - \tan^{2} θ} \neq \tan 4 θ$

So, it is false.

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Most popular questions from this chapter

solve each equation on the interval

$\sqrt{3} \sin θ + \cos θ = 1$

$\tan \frac{θ}{2} = \frac{1 - \cos θ}{_____}$ .

solve each equation on the interval $0 \leq θ < 2 π$

$\sin θ - \sqrt{3} \cos θ = 1$

Show that $\tan^{- 1} (\frac{1}{v}) = \frac{π}{2} - \tan^{- 1} v$ , if $v > 0$

In Problems 9–36, find the exact value of each expression.

$\cos (\sin^{- 1} \frac{\sqrt{2}}{2})$

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