1. Tardigrade
  2. Question
  3. Mathematics
  4. (tan-1 (√3) - sec-1(-2)/cosec-1(-√2) + cos-1 (-(1)2)) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\frac{tan^{-1} \left(\sqrt{3}\right) - sec^{-1}\left(-2\right)}{cosec^{-1}\left(-\sqrt{2}\right) + cos^{-1} \left(-\frac{1}{2}\right)} $ is equal to

MHT CETMHT CET 2016

Solution:

$\frac{\tan ^{-1}(\sqrt{3})-\sec ^{-1}(-2)}{\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(-\frac{1}{2}\right)}$
$=\frac{\tan ^{-1}(\sqrt{3})-\left(\pi-\sec ^{-1}(2)\right)}{-\operatorname{cosec}^{-1}(\sqrt{2})+\pi-\cos ^{-1}\left(\frac{1}{2}\right)}$
$=\frac{\frac{\pi}{3}-\left(\pi-\frac{\pi}{3}\right)}{-\frac{\pi}{4}+\pi-\frac{\pi}{3}}=\frac{\frac{2 \pi}{3}-\pi}{\pi-\frac{\pi}{4}-\frac{\pi}{3}}$
$=\frac{\frac{-\frac{\pi}{3}}{12 \pi-3 \pi-4 \pi}}{12}=\frac{-\frac{\pi}{3}}{\frac{5 \pi}{12}}=-\frac{4}{5}$