Quantitative Aptitude Ques 1272

Question: Evaluate $ \frac{1-{{\tan }^{2}}30{}^\circ }{1+\tan 30{}^\circ }. $

Options:

A) 1/2

B) 2

C) 1/3

D) 3

Show Answer

Answer:

Correct Answer: A

Solution:

  • Given expression, $ \frac{1-{{\tan }^{2}}30{}^\circ }{1+{{\tan }^{2}}30{}^\circ } $ $ =\frac{1-{{( \frac{1}{\sqrt{3}} )}^{2}}}{1+{{( \frac{1}{\sqrt{3}} )}^{2}}} $ $ [ \because \tan 30{}^\circ =\frac{1}{\sqrt{3}} ] $ $ =\frac{1-\frac{1}{3}}{1+\frac{1}{3}}=\frac{2/3}{4/3}=\frac{2}{3}\times \frac{3}{4}=\frac{1}{2} $
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