The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

If $\tan A<0$ and $\tan 2 A=-\frac{4}{3}$, then $\cos 6 A=$

If $m \cos (\alpha+\beta)-n \cos (\alpha-\beta)$ $=m \cos (\alpha-\beta)+n \cos (\alpha+\beta)$, then $\tan \alpha \tan \beta=$