Explanation

(c)
Now, on taking option one by one, we get
(a)$\sin 15{^\circ} = \sin{(45{^\circ} - 30{^\circ}) = \ \frac{\sqrt{3} - 1}{2\sqrt{2}} = irrational}$
(b)$\cos{15{^\circ} = \cos{(45{^\circ} - 30{^\circ}) = \ \frac{\sqrt{3} + 1}{2\sqrt{2}} = irrational}}$
(c)$\sin{15{^\circ}}\cos{15{^\circ} = \frac{1}{2}}(2\sin{15{^\circ}\cos{15{^\circ})}}$
$= \ \frac{1}{2}\sin{30{^\circ} = \ \frac{1}{4} = rational}$
(d)$\sin{15{^\circ}\cos{75{^\circ} = \sin{15{^\circ}\sin{15{^\circ} = \sin^{2}{15{^\circ}}}}}}$
$= \left( \frac{\sqrt{3\ } - 1}{2\sqrt{2}} \right)^{2} = \frac{4 - 2\sqrt{3}}{8} = irrational$