If $\cos A+\cos B+\cos C=0=\sin A+\sin B+\sin C$, then $\cos (A-B)+\cos (B-C)+\cos (C-A)=$

If $\sin x \cdot \cosh y=\cos \theta$ and $\cos x \cdot \sinh y=\sin \theta$, then $\sin ^2 x+\cosh ^2 y=$

The quadratic equation whose roots are $\sin ^2 18^{\circ}$ and $\cos ^2 36^{\circ}$ is

If $\cos \theta=\frac{-3}{5}$ and $\pi<\theta<\frac{3 \pi}{2}$, then $\tan \frac{\theta}{2}+\sin \frac{\theta}{2}+2 \cos \frac{\theta}{2}=$