Question

The value of the expression $\frac{(1+\tan \frac{\pi }{6})(1-\cot \frac{\pi }{6})}{(1+\cos \frac{\pi }{3})(1-\sec \frac{\pi }{3})}$ is

• A. $\frac{4}{3\sqrt{3}}$
• B. $\sqrt{3}$
• C. $\frac{4}{\sqrt{3}}$
• D. $3\sqrt{3}$

Answer 1

The correct option is A $\frac{4}{3\sqrt{3}}$

$k=\frac{(1+\tan \frac{\pi }{6})(1-\cot \frac{\pi }{6})}{(1+\cos \frac{\pi }{3})(1-\sec \frac{\pi }{3})}$
$=\frac{(1+\frac{1}{\sqrt{3}})(1-\sqrt{3})}{(1+\frac{1}{2})(1-2)}$
$=\frac{\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)(\sqrt{3}-1)}{\frac{3}{2}}$
$=\frac{4}{3\sqrt{3}}$