If $\sin ^{2} \theta+3 \cos \theta=2,$ then $\cos ^{3} \theta+\sec ^{3} \theta$ is equal to

If $\sin x + \sin y = \frac{7}{5}$ and $\cos x + \cos y = \frac{1}{5}$,then $\sin(x + y)$ equals

If $\tan \theta_1 = k \cot \theta_2$,then $\frac{\cos (\theta_1 + \theta_2)}{\cos (\theta_1 - \theta_2)} = $

If $0 < \theta < \frac{\pi}{2}$ and $\tan 3 \theta \neq 0$, then $\tan \theta + \tan 2 \theta + \tan 3 \theta = 0$ if $\tan \theta \cdot \tan 2 \theta = k$, where $k =$

$\frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\frac{1}{\sin 3^{\circ} \sin 4^{\circ}}+\ldots+\frac{1}{\sin 89^{\circ} \sin 90^{\circ}} = ?$

Let $a, b, c$ be three non-zero real numbers such that the equation $\sqrt{3} a \cos x + 2 b \sin x = c$,$x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ has two distinct real roots $\alpha$ and $\beta$ with $\alpha + \beta = \frac{\pi}{3}$. Then the value of $\frac{b}{a}$ is