If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y$$ $$9 x^2-6 x y \cos \alpha+y^2$$ is equal to

If $$\mathrm{f}(1)=1, \mathrm{f}^{\prime}(1)=3$$, then the derivative of $$\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$$ at $$x=1$$ is

Three fair coins numbered 1 and 0 are tossed simultaneously. Then variance Var (X) of the probability distribution of random variable $$\mathrm{X}$$, where $$\mathrm{X}$$ is the sum of numbers on the uppermost faces, is

$$\int \frac{1}{\sin (x-a) \sin x} d x=$$