The solution of the equation $4\cos^2 x + 6\sin^2 x = 5$ is:

Find the general solution of $\csc x = -2$.

The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2x + \cos ^4 x + \sin ^4 x + \cos ^6 x + \sin ^6 x = 2$ in the interval $[0, 2\pi]$ is

If $\alpha, \beta, \gamma$ and $\delta$ are the solutions of the equation $\tan \left( \theta + \frac{\pi}{4} \right) = 3 \tan 3\theta$,no two of which have equal tangents,then the value of $\tan \alpha + \tan \beta + \tan \gamma + \tan \delta$ is

Suppose $\theta \in \left[0, \frac{\pi}{4}\right]$ is a solution of $4 \cos \theta - 3 \sin \theta = 1$. Then $\cos \theta$ is equal to:

The number of solutions of the equation $\sin 7 \theta - \sin 3 \theta = \sin 4 \theta$ that lie in the interval $(0, \pi)$ is