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Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80&de...

Simplify \frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}

A.

3\sqrt{2}

B.

2\sqrt{3}

C.

\sqrt{3}

D.

\sqrt{2}

Correct answer is C

\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}

\implies \frac{\tan 80 - \tan 20}{1 + \tan 80 \tan 20} = \tan (80 - 20) = \tan 60°

\tan 60 = \frac{\sin 60}{\cos 60} = \frac{\sqrt{3}}{2} ÷ \frac{1}{2}

= \sqrt{3}