Class 11MathematicsTrigonometrical Ratios, Functions and IdentitiesFundamental trigonometrical ratios and functions, Trigonometrical ratio of allied angles
EasyProve that: $\cot ^{2} \frac{\pi}{6} + \csc \frac{5 \pi}{6} + 3 \tan ^{2} \frac{\pi}{6} = 6$
(N/A) $L.H.S. = \cot ^{2} \frac{\pi}{6} + \csc \frac{5 \pi}{6} + 3 \tan ^{2} \frac{\pi}{6}$
$= (\sqrt{3})^{2} + \csc \left(\pi - \frac{\pi}{6}\right) + 3 \left(\frac{1}{\sqrt{3}}\right)^{2}$
$= 3 + \csc \frac{\pi}{6} + 3 \times \frac{1}{3}$
$= 3 + 2 + 1 = 6$
$= R.H.S.$
$= (\sqrt{3})^{2} + \csc \left(\pi - \frac{\pi}{6}\right) + 3 \left(\frac{1}{\sqrt{3}}\right)^{2}$
$= 3 + \csc \frac{\pi}{6} + 3 \times \frac{1}{3}$
$= 3 + 2 + 1 = 6$
$= R.H.S.$
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