Maths Olympiad Prep

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Algebra Difficulty 2.8 Junior Find the answer

The expression tan⁡12∘+tan⁡18∘1−tan⁡12∘⋅tan⁡18∘=\dfrac {\tan 12 ^{\circ} +\tan 18 ^{\circ} }{1-\tan 12 ^{\circ} \cdot \tan 18 ^{\circ} }= ( ) is equal to:

Pick one

Solution

Solution: tan⁡12∘+tan⁡18∘1−tan⁡12∘⋅tan⁡18∘=tan⁡(12∘+18∘)=tan⁡30∘=33\dfrac {\tan 12 ^{\circ} +\tan 18 ^{\circ} }{1-\tan 12 ^{\circ} \cdot \tan 18 ^{\circ} }=\tan (12^{\circ}+18^{\circ})=\tan 30^{\circ}= \dfrac { \sqrt {3}}{3}.

Hence, the answer is C\boxed{C}.

By using the given conditions and the trigonometric identity for the tangent of the sum of two angles, we find the value of the required expression.

This problem primarily tests the application of the trigonometric identity for the tangent of the sum of two angles, examining the ability to transform thinking, and is considered a basic question.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.