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  4. The value of 2 cot 2 ((π /6))+ 4 tan 2( (π /6)) -3 textcosec (π/6) is

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Q. The value of $ 2{{\cot }^{2}}\,(\frac{\pi} {6})+\,4\,{{\tan }^{2}}(\frac {\pi} {6}) $ $ -3\,\text{cosec }\frac {\pi}{6} $ is

J & K CETJ & K CET 2014Trigonometric Functions

Solution:

$ 2{{\cot }^{2}}\left( \frac{\pi }{6} \right)+4\,{{\tan }^{2}}\left( \frac{\pi }{6} \right)-3\text{cosec}\frac{\pi }{6} $
$=2{{(\sqrt{3})}^{2}}+4{{\left( \frac{1}{\sqrt{3}} \right)}^{2}}-3(2)=2\times 3+\frac{4}{3}-6=\frac{4}{3} $