question_answer

Equation of the image of the line \[x+y={{\sin }^{-1}}({{a}^{3}}+1)+co{{s}^{-1}}({{a}^{2}}+1)-{{\tan }^{-1}}(a+1),\]\[a\in R\] about y-axis is given by-

A) \[x-y+\frac{\pi }{4}=0\]

B) \[x-y=0\]

C) \[x-y=\frac{\pi }{4}\]

D) \[x-y=\frac{\pi }{2}\]

Correct Answer: A

Solution :

a=0

equation \[x+y=\frac{\pi }{2}-\frac{\pi }{4}\]      \[\Rightarrow x+y=\frac{\pi }{4}\]

image \[x-y+\frac{\pi }{4}=0\]