If the period of the function $f(x)=\frac{\tan 5 x \cos 3 x}{\sin 6 x}$ is $\alpha$, then $f\left(\frac{\alpha}{8}\right)=$

If $\sin x+\sin y=\alpha, \cos x+\cos y+\beta$, then $\operatorname{cosec}(x+y)=$

If $P+Q+P=\frac{\pi}{4}$, then $\cos \left(\frac{\pi}{8}-P\right)+\cos \left(\frac{\pi}{8}-Q\right)+\cos$ $\left(\frac{\pi}{8}-R\right)=$

If $\theta$ is an acute angle, $\cosh x=K$ and $\sinh x=\tan \theta$, then $\sin \theta=$