Question

If $x={30}^o$, verify that $\cos 3x=4{\cos }^{3}x-3\cos x$.

Answer 1

$x=30°\left(\text{Given}\right)$

Now,

$\cos 3x=4{\cos }^{3}x-3\cos x$

$\cos (3\times 30°)=4{\cos }^{3}30°-3\cos 30°$

$\cos 90°=4{\left(\frac{\sqrt{3}}{2}\right)}^3-3\left(\frac{\sqrt{3}}{2}\right)$

$0=4\left(\frac{3\sqrt{3}}{8}\right)-\frac{3\sqrt{3}}{2}$

$0=\frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}$

$0=0$

L.H.S. $=$ R.H.S.

Hence verified that $\cos 3x=4{\cos }^{3}x-3\cos x$.