Question

prove that: cot^2pi/6+cosec5pi/6+3tan^2pi/6=6

Answer 1

Answer:

see the picture part

Step-by-step explanation:

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Answer 2

Question :-

Prove that :-

$\\ \implies \sf \bf { \cot }^{2} \dfrac{ \pi}{6} + \csc \dfrac{5 \pi}{6} + 3 { \tan }^{2} \dfrac{ \pi}{6} = 6$

Solution :-

Taking LHS :-

$\large\implies \sf \bf { \cot }^{2} \dfrac{ \pi}{6} + \csc \dfrac{5 \pi}{6} + 3 { \tan }^{2} \dfrac{ \pi}{6}$

$\\ \\ \large\implies \bf \sf { \cot}^{2} \frac{ \pi}{6} + \csc \bigg( \pi - \frac{ \pi}{6} \bigg) + 3 { \tan }^{2} \frac{ \pi}{6}$

$\\ \\ \large \implies \bf \sf \frac{ \pi}{6} + \csc \frac{ \pi}{6} + 3 { \tan }^{2} \frac{ \pi}{6}$

$\\ \\ \large\implies \bf \sf {( \sqrt{3} )}^{2} + 2 + 3 {\bigg( \frac{1}{ \sqrt{3} } \bigg)}^{2}$

$\\ \\ \large \implies \sf \bf3 + 2 + \cancel3 \times \frac{1}{ \cancel3}$

$\\ \\ \large \implies \bf3 + 2 + 1 = 6$

LHS = RHS

Hence proved !!