If 20^ + 40^ +3 20 40^ is equal to: - Vidyadip

MCQ

If $\tan20^\circ+\tan40^\circ+\sqrt{3}\tan20\circ\tan40^\circ$ is equal to:

A
$\frac{\sqrt{3}}{4}$
B
$\frac{\sqrt{3}}{2}$
✓
$\sqrt{3}$
D
$1$

✓

Answer

Correct option: C.

$\sqrt{3}$

$\tan20^\circ+\tan40^\circ+\sqrt{3}\tan20^\circ\tan40^\circ$
$=\tan60^\circ(1-\tan20^\circ\tan40^\circ)+\tan60^\circ\tan20^\circ\tan40^\circ$
$=\tan60^\circ-\tan60^\circ\tan20^\circ\tan40^\circ+\tan60^\circ\tan20^\circ\tan40^\circ$
$=\tan60^\circ$
$=\sqrt{3}$

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