What is the value

Question:

What is the value of $\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)+\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right) ?$

Solution:

$\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)+\sin ^{-1}\left(\sin \frac{2 \pi}{3}\right)$

$=\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)+\sin ^{-1}\left\{\sin \left(\pi-\frac{\pi}{3}\right)\right\}$

$=\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)+\sin ^{-1}\left\{\sin \left(\frac{\pi}{3}\right)\right\}$

$\left[\because\right.$ Range of sine is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] ; \frac{\pi}{3} \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ and range of cosine is $\left.[0, \pi] ; \frac{2 \pi}{3} \in[0, \pi]\right]$

$=\frac{2 \pi}{3}+\frac{\pi}{3}$

$=\pi$

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now