Let $$(x,y)$$ be such that $${\sin ^{ - 1}}(ax) + {\cos ^{ - 1}}(y) + {\cos ^{ - 1}}(bxy) = {\pi \over 2}$$.

Match the statements in Column I with the statements in Column II.

	Column I		Column II
(A)	If $$a=1$$ and $$b=0$$, then $$(x,y)$$	(P)	lies on the circle $$x^2+y^2=1$$
(B)	If $$a=1$$ and $$b=1$$, then $$(x,y)$$	(Q)	lies on $$(x^2-1)(y^2-1)=0$$
(C)	If $$a=1$$ and $$b=2$$, then $$(x,y)$$	(R)	lies on $$y=x$$
(D)	If $$a=2$$ and $$b=2$$, then $$(x,y)$$	(S)	lies on $$(4x^2-1)(y^2-1)=0$$

Let F(x) be an indefinite integral of $$\sin^2x$$.

Statement 1 : The function F(x) satisfies F($$x+\pi$$) = F($$x$$) for all real x.

Statement 2 : $${\sin ^2}(x + \pi ) = {\sin ^2}x$$ for all real x.

The value of $$x$$ for which $$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}\,x} \right)$$ is

If $${\sin ^{ - 1}}\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 4} - ....} \right)$$ $$$ + {\cos ^{ - 1}}\left( {{x^2} - {{{x^4}} \over 2} + {{{x^6}} \over 4} - ....} \right) = {\pi \over 2}$$$
for $$0 < \left| x \right| < \sqrt 2 ,$$ then $$x$$ equals