Question

${\cot }^2\frac{\pi }{6}+\mathrm{cosec}\frac{5\pi }{6}+3{\tan }^2\frac{\pi }{6}$ is equal to

• A. 1
• B. 5
• C. 3
• D. 6

Answer 1

Answer: (D)

${\cot }^2\frac{\pi }{6}+cosec\frac{5\pi }{6}+3{\tan }^2\frac{\pi }{6}$
$=(\sqrt{3}{)}^2+cosec\left(\pi -\frac{\pi }{6}\right)+3{\left(\frac{1}{\sqrt{3}}\right)}^2$
$=3+cosec\frac{\pi }{6}+1=3+2+1=6$