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

The number of real solutions of
$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} + x + 1} = \pi /2$$ is