Question

If x = ${30}^{\circ }$ verify that
sin 3x = 3 sin x - 4 $si{n}^3$x

Answer 1

(i) $\sin (3\times 30°)=\sin 90°=1$

(ii) $3\sin 30°-4{\left(\sin 30°\right)}^3=3\times \left(\frac{1}{2}\right)-4{\left(\frac{1}{2}\right)}^3=\frac{3}{2}-\frac{1}{2}=\frac{2}{2}=1$