If $\sec \theta + \tan \theta = \sqrt{3},$ then the positive value of $\sin \theta$ is :$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$\frac{1}{\sqrt{3}}$$\sqrt{3}$

If $x=\cos1^{\circ} \cdot \cos2^{\circ} \cdot \cos3^{\circ}\dots\cos89^{\circ}$ and $y=\cos2^{\circ}\cos6^{\circ}\cos10^{\circ}\dots\cos86^{\circ}$ then what the integer ...