The exact value of $\cos^2 73^\circ + \cos^2 47^\circ + (\cos 73^\circ \cdot \cos 47^\circ)$ is

If $0 \leq x \leq 3$ and $0 \leq y \leq 3$,then the number of solutions $(x, y)$ of the equation $\left(\sqrt{\sin^2 x - \sin x + \frac{1}{2}}\right) 2^{\sec^2 y} = 1$ is

If $x=\frac{\sin^3 \theta}{\cos^2 \theta}$ and $y=\frac{\cos^3 \theta}{\sin^2 \theta}$,where $\sin \theta+\cos \theta=\frac{1}{2}$,then $x+y=$

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

The number of elements in the set $S = \{\theta \in [-4\pi, 4\pi] : 3 \cos^2 2\theta + 6 \cos 2\theta - 10 \cos^2 \theta + 5 = 0\}$ is

If $\sin x + \sin y = \frac{\sqrt{3}+1}{2}$ and $\cos x + \cos y = \frac{\sqrt{3}-1}{2}$,then $\tan^2 \left(\frac{x-y}{2}\right) + \tan^2 \left(\frac{x+y}{2}\right) = $