Question

The value of $\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)$ is equal to

• A. $-\frac{\pi}{4}$
• B. $-\frac{\pi}{8}$
• C. $-\frac{5 \pi}{12}$
• D. $-\frac{4 \pi}{9}$

Answer 1

Answer: (B)

$\tan ^{-1}\left[\frac{\cos \left(4 \pi-\frac{\pi}{4}\right)-1}{\sin \frac{\pi}{4}}\right]$
$\Rightarrow \tan ^{-1}\left(\frac{\cos \frac{\pi}{4}-1}{\sin \frac{\pi}{4}}\right)$
$\tan ^{-1}\left(\frac{1-\sqrt{2}}{1}\right)=-\frac{\pi}{8}$