The number of real solutions of

$\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^2+x+1}=\frac{\pi}{2}$ is

The value of $\sin \left(2 \cos ^{-1}\left(-\frac{3}{5}\right)\right)$ is

If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is

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