If $\sec \theta + \tan \theta = p,$ then $\tan \theta$ is equal to

The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \cos (\lambda \alpha)}{\sin \alpha \cos \alpha} = \lambda - 1$ holds for all real $\alpha$ which are not integral multiples of $\pi/2$ is:

If $5(\tan^2 x - \cos^2 x) = 2\cos 2x + 9$,then $\cos 4x$ is equal to

Let $A = \{x \in R : |\sqrt{3} \cos x - \sin x| \geq 2, 0 \leq x \leq 2\pi\}$. If $x_1 \in A$ and $x_2 \in A$,then find the possible value of $\frac{x_1}{x_2}$.

$\frac{\tan A}{1-\cot A} + \frac{\cot A}{1-\tan A} = ?$

If $\tanh x = \operatorname{sech} y = \frac{3}{5}$ and $e^{x+y}$ is an integer,then $e^{x+y} =$