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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

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

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

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

= \(\sqrt{3}\)