If $\tan A + \cot A = 2$,then the value of $\tan^{10} A + \cot^{10} A$ is

Without using trigonometric tables,evaluate: $\sin 48^{\circ} \sec 42^{\circ} + \cos 48^{\circ} \operatorname{cosec} 42^{\circ} = $

The maximum value of $\cos \alpha_1 \cdot \cos \alpha_2 \cdots \cos \alpha_n$ under the restrictions $0 \le \alpha_1, \alpha_2, \dots, \alpha_n \le \frac{\pi}{2}$ and $\cot \alpha_1 \cdot \cot \alpha_2 \cdots \cot \alpha_n = 1$ is

If $\alpha$ is a root of $25\cos^2\theta + 5\cos\theta - 12 = 0$ and $\pi/2 < \alpha < \pi$,then $\sin 2\alpha$ is equal to

$\alpha, \beta, \gamma$ are real numbers satisfying $\alpha + \beta + \gamma = \pi$. The minimum value of the expression $\sin \alpha + \sin \beta + \sin \gamma$ is

Let $A, B, C$ be three angles such that $\sin A + \sin B + \sin C = 0$. Then,$\frac{\sin A \sin B \sin C}{\sin 3A + \sin 3B + \sin 3C}$ (wherever defined) is equal to: