If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possible values of $\tan A$ are

The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is

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 $\sin (x-y)+\cos (x-y)=$