Search any question & find its solution
Question:
Answered & Verified by Expert
Prove that:
$\cot ^2 \frac{\pi}{6}+\operatorname{cosec} \frac{5 \pi}{6}+3 \tan ^2 \frac{\pi}{6}=6$
$\cot ^2 \frac{\pi}{6}+\operatorname{cosec} \frac{5 \pi}{6}+3 \tan ^2 \frac{\pi}{6}=6$
Solution:
1759 Upvotes
Verified Answer
L.H.S. $=\cot ^2 \frac{\pi}{6}+\operatorname{cosec} \frac{5 \pi}{6}+3 \tan ^2 \frac{\pi}{6}$
$=\left(\cot \frac{\pi}{6}\right)^2+\operatorname{cosec}\left(\pi-\frac{\pi}{6}\right)+3\left(\tan \frac{\pi}{6}\right)^2$
$=(\sqrt{3})^2+\operatorname{cosec} \frac{\pi}{6}+3\left(\frac{1}{\sqrt{3}}\right)^2$
$=3+2+3 \times \frac{1}{3}=3+2+1=6=$ R.H.S.
$=\left(\cot \frac{\pi}{6}\right)^2+\operatorname{cosec}\left(\pi-\frac{\pi}{6}\right)+3\left(\tan \frac{\pi}{6}\right)^2$
$=(\sqrt{3})^2+\operatorname{cosec} \frac{\pi}{6}+3\left(\frac{1}{\sqrt{3}}\right)^2$
$=3+2+3 \times \frac{1}{3}=3+2+1=6=$ R.H.S.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.