If $\frac{\sin^4 x}{2} + \frac{\cos^4 x}{3} = \frac{1}{5}$,then $27 \sec^6 x + 8 \operatorname{cosec}^6 x = $

The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + \dots + \sin 360^\circ$ is

If $\frac{2 \sin \alpha}{1+\cos \alpha+\sin \alpha}=x$,then $\frac{1-\cos \alpha-\sin \alpha}{\cos \alpha}=$

If $2 \cos \theta + \sin \theta = 1$ $\left( \theta \neq \frac{\pi}{2} \right)$,then $7 \cos \theta + 6 \sin \theta$ is equal to

The value of $\frac{\sin^2 \theta}{\sin \theta - \cos \theta} - \frac{\sin \theta + \cos \theta}{\tan^2 \theta - 1}$ for all permissible values of $\theta$ is:

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