Write the value

Question:

Write the value of $\tan ^{-1}\left\{\tan \left(\frac{15 \pi}{4}\right)\right\}$.

Solution:

We have

$\tan ^{-1}\left\{\tan \left(\frac{15 \pi}{4}\right)\right\}=\tan ^{-1}\left\{\tan \left(4 \pi-\frac{\pi}{4}\right)\right\}$

$\tan ^{-1}\left\{-\tan \left(\frac{\pi}{4}\right)\right\} \quad[\because \tan (4 \pi-x)=-\tan x]$

$=\tan ^{-1}\left\{\tan \left(-\frac{\pi}{4}\right)\right\}$

$=-\frac{\pi}{4} \quad\left[\because \tan ^{-1}(\tan x)=x\right]$

$\therefore \tan ^{-1}\left\{\tan \left(\frac{15 \pi}{4}\right)\right\}=-\frac{\pi}{4}$

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