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

Assessment: WAEC SSCE - Further Mathematics - 2007 (Objective) Subject: Further Mathematics

Question 1 Report

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

Answer Details
We can simplify this expression using the trigonometric identity: \[\tan(A-B) = \frac{\tan A - \tan B}{1+\tan A \tan B}\] In this case, we have A = 80° and B = 20°. Therefore: \[\tan(A-B) = \tan(80°-20°) = \tan 60° = \sqrt{3}\] Using the identity, we can rewrite the expression as: \[\frac{\tan 80° - \tan 20°}{1 + \tan 80° \tan 20°} = \tan(80°-20°) = \sqrt{3}\] Therefore, the simplified expression is \(\sqrt{3}\). So the correct option is (3) \(\sqrt{3}\).

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