If $\sec x+\tan x=2,0 < x < \frac{\pi}{2}$ then $\sin \frac{x}{4}=$

The maximum value of the function $a \sin x+b \cos x$ is

If $\sin \theta=\frac{1}{2}\left(x+\frac{1}{x}\right)$, then $\sin 3 \theta+\frac{1}{2}\left(x^3+\frac{1}{x^3}\right)=$

If $\sin \mathrm{A}+\sin \mathrm{B}=x$ and $\cos \mathrm{A}+\cos \mathrm{B}=y$, then $\sin (A+B)=$