Simplify \(\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°}\)
FURTHER MATHEMATICS
WAEC 2007
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: C. \(\sqrt{3}\)
Explanation
\(\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}\)
\(\implies \frac{\tan 80 - \tan 20}{1 + \tan 80 \tan 20} = \tan (80 - 20) = \tan 60°\)
\(\tan 60 = \frac{\sin 60}{\cos 60} = \frac{\sqrt{3}}{2} ÷ \frac{1}{2}\)
= \(\sqrt{3}\)
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