If the line x = $$\alpha $$ divides the area of region R = {(x, y) $$ \in $$R² : x³ $$ \le $$ y $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ 1} into two equal parts, then

Let $$\alpha $$ and $$\beta $$ be non zero real numbers such that $$2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \beta = 1$$. Then which of the following is/are true?

Let $$f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$$

for x $$ \ne $$ 1. Then

If $$g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt$$, then