JEE Math Practice Question

Which of the following statements is correct for the function g($$\alpha$$) for $$\alpha$$ $$\in$$ R such that $$g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx} $$

1. A.$$g(\alpha )$$ is a strictly increasing function
2. B.$$g(\alpha )$$ is an even function
3. C.$$g(\alpha )$$ has an inflection point at $$\alpha$$ = $$-$$$${1 \over 2}$$
4. D.$$g(\alpha )$$ is a strictly decreasing function