Prove that :
$\cot ^{2} \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}=6$
Prove that :
$\cot ^{2} \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}=6$
$L.H.S.$ $=\cot ^{2}\, \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}$
$=(\sqrt{3})^{2}+\cos ec\, \left(\pi-\frac{\pi}{6}\right)+3\left(\frac{1}{\sqrt{3}}\right)^{2}$
$=3+\cos ec\, \frac{\pi}{6}+3 \times \frac{1}{3}$
$=3+2+1=6$
$= R . H.S$
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