The number of solutions of the equation $32^{\tan^{2} x} + 32^{\sec^{2} x} = 81$ for $0 \leq x \leq \frac{\pi}{4}$ is:

The smallest integer $n$ such that $\frac{1}{\sin 45^{\circ} \sin 46^{\circ}}+\frac{1}{\sin 47^{\circ} \sin 48^{\circ}}+\ldots+\frac{1}{\sin 133^{\circ} \sin 134^{\circ}}=\frac{1}{\sin \left(n^{\circ}\right)}$ is

In a triangle $ABC$,if $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$,then $\sin (A + B)$ is equal to

If $\tan \theta_1 = k \cot \theta_2$,then $\frac{\cos (\theta_1 + \theta_2)}{\cos (\theta_1 - \theta_2)} = $

The value of the expression $\frac{(\sin 36^{\circ} + \cos 36^{\circ} - \sqrt{2} \sin 27^{\circ})^2}{2 \sin 54^{\circ}}$ is less than

In $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{(\sin^2 A + \sin^2 B)}{(\sin^2 A - \sin^2 B)} \sin(A - B) = $