| Evaluate \[\frac{1-{{\tan }^{2}}30{}^\circ }{1+\tan 30{}^\circ }.\] |
A) 1/2
B) 2
C) 1/3
D) 3
Correct Answer: A
Solution :
| Given expression, \[\frac{1-{{\tan }^{2}}30{}^\circ }{1+{{\tan }^{2}}30{}^\circ }\] |
| \[=\frac{1-{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}}{1+{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}}\] \[\left[ \because \tan 30{}^\circ =\frac{1}{\sqrt{3}} \right]\] |
| \[=\frac{1-\frac{1}{3}}{1+\frac{1}{3}}=\frac{2/3}{4/3}=\frac{2}{3}\times \frac{3}{4}=\frac{1}{2}\] |
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