Question

Equation of image of line $x+y={\sin }^{-1}(a^6+1)+{\cos }^{-1}(a^4+1)-{\tan }^{-1}(a^2+1),a\in R$ 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

The correct option is D $x-y=\frac{\pi }{4}$

$-1\le a^6+1\le 1\Rightarrow a^6\le 0\Rightarrow a^6=0$
$\Rightarrow a=0\Rightarrow x+y={\sin }^{-1}1+{\cos }^{-1}1-{\tan }^{-1}1$
$\Rightarrow x+y=\frac{\pi }{4}$

Image is,

$x-y=\frac{\pi }{4}$