jee-advanced 2007 Q63

jee-advanced · India · paper1 Composite & Inverse Functions Find or Apply an Inverse Function Formula
The number of solutions of the equation $\sin^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right) - \sin^{-1}\left(\frac{1}{\sqrt{1+x^2}}\right) = \sin^{-1}\left(\frac{x-1}{\sqrt{1+(x-1)^2}}\right) - \sin^{-1}\left(\frac{1}{\sqrt{1+(x-1)^2}}\right)$ is
(A) 0
(B) 1
(C) 2
(D) infinite 
The number of solutions of the equation $\sin^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right) - \sin^{-1}\left(\frac{1}{\sqrt{1+x^2}}\right) = \sin^{-1}\left(\frac{x-1}{\sqrt{1+(x-1)^2}}\right) - \sin^{-1}\left(\frac{1}{\sqrt{1+(x-1)^2}}\right)$ is\\
(A) 0\\
(B) 1\\
(C) 2\\
(D) infinite
Paper Questions
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