If $\frac{x^2-3}{(x+2)\left(x^2+1\right)}=\frac{A}{x+2}+\frac{B x+C}{\left(x^2+1\right)}$, then $3 A+2 B-C=$

If $5 \sin \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between $\alpha$ and $\beta$ (including $\alpha, \beta$ also), then $(\alpha-\beta)(\alpha+\beta-6)=$

$$ \frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots \sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}= $$

If $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$ and $\alpha+\beta \neq \frac{\pi}{2}$, then $\frac{\tan \left(\frac{\pi}{4}-\alpha\right)}{\tan \left(\frac{\pi}{4}-\beta\right)}=$