\[{{\sin }^{-1}}\left( a-\frac{{{a}^{2}}}{3}+\frac{{{a}^{3}}}{9}+... \right)+{{\cos }^{-1}}(1+b+{{b}^{2}}+...)=\frac{\pi }{2}\]when

\[a=\frac{1}{6}\] and \[b=\frac{1}{2}\]

\[{{\sin }^{-1}}\left( a-\frac{{{a}^{2}}}{3}+\frac{{{a}^{3}}}{9}+... \

1.	\[{{\sin }^{-1}}\left( a-\frac{{{a}^{2}}}{3}+\frac{{{a}^{3}}}{9}+... \right)+{{\cos }^{-1}}(1+b+{{b}^{2}}+...)=\frac{\pi }{2}\]when
A.	\[a=-3\] and \[b=1\]
B.	\[a=1\] and \[b=-\frac{1}{3}\]
C.	\[a=\frac{1}{6}\] and \[b=\frac{1}{2}\]
D.	None of these
Answer» C. \[a=\frac{1}{6}\] and \[b=\frac{1}{2}\]

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\[{{\sin }^{-1}}\left( a-\frac{{{a}^{2}}}{3}+\frac{{{a}^{3}}}{9}+... \right)+{{\cos }^{-1}}(1+b+{{b}^{2}}+...)=\frac{\pi }{2}\]when

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