Question

Prove that : ${\cot }^2\frac{\pi }{6}+{\text{cosec}}^2\frac{5\pi }{6}+3{\tan }^2\frac{\pi }{6}=8$

Answer 1

${\cot }^2\frac{\pi }{6}+{\csc }^2\frac{5\pi }{6}+3{\tan }^2\frac{\pi }{6}$

$={\left(\sqrt{3}\right)}^2+2^2+3{\left(\frac{1}{\sqrt{3}}\right)}^2$

$=3+4+1$

$=8$