Choose the correct option and justify your choice:
$fraction numerator 2 tan 30 degree over denominator 1 minus tan squared 30 degree end fraction equals$
(A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°.

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Solution

fraction numerator 2 space tan space 30 degree over denominator 1 minus tan squared 30 degree end fraction space equals space fraction numerator 2 cross times begin display style fraction numerator 1 over denominator square root of 3 end fraction end style over denominator 1 minus open parentheses begin display style fraction numerator 1 over denominator square root of 3 end fraction end style close parentheses squared end fraction space equals space fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator 1 minus begin display style 1 third end style end fraction

equals space fraction numerator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style over denominator begin display style 2 over 3 end style end fraction space equals space fraction numerator 2 over denominator square root of 3 end fraction cross times 3 over 2 space equals space square root of 3 space end root space equals space tan space 60 degree

Ans. (C).

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