If $\sin x \cosh y = \cos \theta$ and $\cos x \sinh y = \sin \theta$,then $\sin^2 x + \cosh^2 y =$

$\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ is equal to

If $\cos \theta = -\frac{\sqrt{3}}{2}$ and $\sin \alpha = -\frac{3}{5}$,where $\theta$ does not lie in the third quadrant,then $\frac{2 \tan \alpha + \sqrt{3} \tan \theta}{\cot^2 \theta + \cos \alpha}$ is equal to

If $x = \sec \phi - \tan \phi$ and $y = \csc \phi + \cot \phi$,then:

In triangles $ABC$ and $DEF$,$AB = DE$,$AC = EF$ and $\angle A = 2\angle E$. The two triangles will have the same area if angle $A$ is equal to:

If $a \tan \alpha + b \tan \beta = (a + b) \tan \left( \frac{\alpha + \beta}{2} \right)$ and $\alpha - \beta \neq 2n\pi$,then $\frac{\cos \beta}{\cos \alpha} = $