Question

Prove that $cot^2 \frac{π}{6}+cosec \frac{5π}{6}+3\,tan^2 \frac{π}{6}=6$

Answer 1

L.H.S. = $cot^2 \frac{π}{6}+cosec \frac{5π}{6}+3\,tan^2 \frac{π}{6}$

$=(√3)^2+cosec({\pi}-\frac{\pi}{6})+3(\frac{1}{√3})^2$

$3+cosec\frac{\pi}{6}+3×\frac{1}{3}$

$3+2+1=6$

$=R.H.S$