Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Using ${\sin }^3\theta =\frac{1}{4}(3\sin \theta -\sin 3\theta )$ : $=\frac{1}{4}\left[3\left(\sin 10^{\circ }+\sin 50^{\circ }-\sin 70^{\circ }\right)-\left(\sin 30^{\circ }+\sin 150^{\circ }-\sin 210^{\circ }\right)\right]$ $\sin 10^{\circ }+\sin 50^{\circ }-\sin 70^{\circ }=\sin 10^{\circ }-2\cos 60^{\circ }\sin 10^{\circ }=0$ and $\sin 30^{\circ }+\sin 150^{\circ }-\sin 210^{\circ }=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{3}{2}$ $=\frac{1}{4}\left[0-\frac{3}{2}\right]=-\frac{3}{8}$