The equation $\sec^2 \theta = \frac{4xy}{(x + y)^2}$ is only possible when

If $\alpha+\beta+\gamma=2 \theta$,then $\cos \theta+\cos (\theta-\alpha)+\cos (\theta-\beta)+\cos (\theta-\gamma)$ is equal to

If $A + B = \pi / 2$,then the maximum value of $\cos A \cos B$ is:

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 $f(x) = \cos^2 x + \sec^2 x$,then

If $A + B + C = \frac{\pi}{2}$,then the value of $\tan A \tan B + \tan B \tan C + \tan C \tan A$ is