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Trigonometry Practice Test 2

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Question : 15 of 22

Marks: +1, -0

The value of tan20° tan40° tan80° is:

$\frac{1}{\sqrt{3}}$
$\sqrt{3}$
$\frac{1}{8}$
$\frac{\sqrt{8}}{8}$

Solution:

Concept:

Use the identity

\tan x \tan(60^\circ-x)\tan(60^\circ+x)=\tan 3x

.

Explanation:

Compare the given angles with

x

,

60^\circ-x

, and

60^\circ+x

.

Let

x=20^\circ

.

Then

60^\circ-x=40^\circ

and

60^\circ+x=80^\circ

.

So

\tan20^\circ\tan40^\circ\tan80^\circ=\tan(3\times20^\circ)

.

This simplifies to

\tan60^\circ

.

Since

\tan60^\circ=\sqrt{3}

, the required value is

\sqrt{3}

.

Answer:

\sqrt{3}

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