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 $\sin (A+B)=$

If $\sin \mathrm{A}=\mathrm{n} \sin (\mathrm{A}+2 \mathrm{~B})$, then $\tan (\mathrm{A}+\mathrm{B})=$

The value of

$$ \begin{aligned} \sin ^2 5^{\circ}+\sin ^2 10^{\circ} & +\sin ^2 15 +\ldots \ldots \ldots \ldots \ldots \ldots+\sin ^2 85^{\circ}+\sin ^2 90^{\circ}= \end{aligned} $$