Question

If $\tan ^{-1}\left(x^2+3|x|-4\right)+\cot ^{-1}\left(4 \pi+\sin ^{-1}(\sin 14)\right)=\frac{\pi}{2}$, then the value of $\sin ^{-1}(\sin 2|x|)$ is equal to

• A. $6-2 \pi$
• B. $2 \pi-6$
• C. $\pi-3$
• D. $3-\pi$

Answer 1

Answer: (D)

$\sin ^{-1}(\sin 14)=(14-4 \pi)$
$\text { So, } x^2+3|x|-4=4 \pi+(14-4 \pi) $
$\Rightarrow x^2+3|x|-18=0 $
$\Rightarrow(|x|+6)(|x|-3)=0 $
$\therefore|x|=3$
So, $\sin ^{-1}(\sin 2|x|)=\sin ^{-1}(\sin 6)=(6-2 \pi)$