Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

(A) $\sin \frac{\pi }{12}\cos \frac{\pi }{12}=\frac{1}{2}\sin \frac{\pi }{6}=\frac{1}{4}$

(B) $-\mathrm{cosec}\frac{\pi }{10}\sec \frac{\pi }{5}=-4$

(C) $1-2{\sin }^2\frac{\pi }{8}{\cos }^2\frac{\pi }{8}=1-\frac{1}{4}=\frac{3}{4}$

(D) $\left(2{\cos }^2\frac{\pi }{9}\right)\left(2{\cos }^2\frac{2\pi }{9}\right)\left(2{\cos }^2\frac{4\pi }{9}\right)=\frac{1}{8}$

All four are rational.