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Question

Prove that:
$c o t^{2} \frac{π}{6} + c o s e c \frac{5 π}{6} + 3 t a n^{2} \frac{π}{6} = 6$

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Solution

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$L H S = c o t^{2} \frac{π}{6} + c o s e c \frac{5 π}{6} + 3 t a n^{2} \frac{π}{6}$

$= {\sqrt{3}}^{2} + c o s e c (π - \frac{π}{6}) + 3 \frac{1}{{\sqrt{3}}^{2}}$
$= 4 + c o s e c \frac{π}{6}$

$= 4 + 2 = 6$

Hence proved.

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