Which of the following number(s) is/are ratio | vedclass

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Question

(C) We evaluate each option:$(a)$ $\sin 15^\circ = \sin(45^\circ - 30^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}$,which is irrational.$(b)$ $\cos 15^\circ

Vedclass · Accepted Answer

$\sin 15^\circ \cos 15^\circ$

Vedclass · Answer

(C) We evaluate each option:$(a)$ $\sin 15^\circ = \sin(45^\circ - 30^\circ) = \frac{\sqrt{6} - \sqrt{2}}{4}$,which is irrational.$(b)$ $\cos 15^\circ = \cos(45^\circ - 30^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4}$,which is irrational.$(c)$ $\sin 15^\circ \cos 15^\circ = \frac{1}{2}(2 \sin 15^\circ \cos 15^\circ) = \frac{1}{2} \sin 30^\circ = \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{4}$,which is rational.$(d)$ $\sin 15^\circ \cos 75^\circ = \sin 15^\circ \sin 15^\circ = \sin^2 15^\circ = \left(\frac{\sqrt{6} - \sqrt{2}}{4}ight)^2 = \frac{6 + 2 - 2\sqrt{12}}{16} = \frac{8 - 4\sqrt{3}}{16} = \frac{2 - \sqrt{3}}{4}$,which is irrational.Thus,the correct option is $(c)$.

Which of the following number$(s)$ is/are rational?

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