Question

Prove that cot ^2 π/6 + cosec 5π/6 + 3 tan ^2 π/6 = 6

Answer 1

SOLUTION

TO PROVE

$cot ^2 \frac{π}{6} + cosec \frac{5π}{6} + 3 tan ^2 \frac{π}{6}$

EVALUATION

$cot ^2 \frac{π}{6} + cosec \frac{5π}{6} + 3 tan ^2 \frac{π}{6}$

$= {cot}^{2} {30}^{ \circ} + {cosec} {150}^{ \circ} +3 {tan}^{2} {30}^{ \circ}$

$= {( \sqrt{3} )}^{2} + sec {60}^{ \circ} + 3 \times {( \frac{1}{ \sqrt{3} })}^{2}$

$= 3 + 2 + 1 = 6$

Hence proved

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