If $\alpha+\beta+\gamma=\pi$, then the expression $\sin ^2 \alpha+\sin ^2 \beta-\sin ^2 \gamma$ has the value

If $$\mathrm{a} \cos 2 \theta+\mathrm{b} \sin 2 \theta=\mathrm{c}$$ has $$\alpha$$ and $$\beta$$ as its roots, then the value of $$\tan \alpha+\tan \beta$$ is

If $$\sin (\theta-\alpha), \sin \theta$$ and $$\sin (\theta+\alpha)$$ are in H.P., then the value of $$\cos 2 \theta$$ is

The value of $$\begin{aligned} \cos \left(18^{\circ}-\mathrm{A}\right) \cdot \cos ( & \left.18^{\circ}+\mathrm{A}\right) \\ & -\cos \left(72^{\circ}-\mathrm{A}\right) \cos \left(72^{\circ}+\mathrm{A}\right) \text { is }\end{aligned}$$