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3.Trigonometrical Ratios, Functions and Identities

easy

Prove that :

$\cot ^{2} \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}=6$

Option A

Option B

Option C

Option D

Solution

$L.H.S.$ $=\cot ^{2}\, \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}$

$=(\sqrt{3})^{2}+\cos ec\, \left(\pi-\frac{\pi}{6}\right)+3\left(\frac{1}{\sqrt{3}}\right)^{2}$

$=3+\cos ec\, \frac{\pi}{6}+3 \times \frac{1}{3}$

$=3+2+1=6$

$= R . H.S$

Std 11

Mathematics

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