Question

Equation of the image of the line $x+y=\sin ^{-1}\left(a^6+1\right)+\cos ^{-1}\left(a^4+1\right)-\tan ^{-1}\left(a^2+1\right), a \in R$ about $x$ axis is given by

• A. $x-y=0$
• B. $x-y=\frac{\pi}{2}$
• C. $x-y=\pi$
• D. $ x-y=\frac{\pi}{4}$

Answer 1

Answer: (D)

$\therefore \sin ^{-1} \text { is defined for }[-1,1] $
$\therefore a =0 $
$\therefore x + y =\sin ^{-1} 1+\cos ^{-1} 1-\tan ^{-1} 1=\frac{\pi}{4}$
Clearly image about $x$ axis will be $x-y=\frac{\pi}{4}$