If $P=\operatorname{cosec} \frac{\pi}{8}+\operatorname{cosec} \frac{2 \pi}{8}+\operatorname{cosec} \frac{3 \pi}{8}$ $+\operatorname{cosec} \frac{13 \pi}{8}+\operatorname{cosec} \frac{14 \pi}{8}+\operatorname{cosec} \frac{15 \pi}{8}$ and $\phi=8 \sin \frac{\pi}{18} \sin \frac{5 \pi}{18} \sin \frac{7 \pi}{18}$, then the value of $P+Q$ is

Difference between the maximum and minimum values of $f(x)=-\sin ^3 x+3 \sin ^2 x+5$ in $x \in\left[0, \frac{\pi}{2}\right]$ is

If $e$ is the eccentricity of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\theta$ is the angle between the asymptotes, then $\cos \frac{\theta}{2}$ is

If tangent to the curve $f(x)=x^3-\alpha x^2-x+\beta$ at point $(1,3)$ on the curve, cut equals non zero intercepts on co-ordinate axes, then