The value of $4 \cos ^3 20^{\circ}$ is

The value of $4 \cos ^3 20^{\circ}$ is
  1. $-\frac{1}{2}-\cos 20^{\circ}$
  2. $-\frac{1}{2}+3 \cos 20^{\circ}$
  3. $\frac{1}{2}+3 \cos 20^{\circ}$
  4. $\frac{1}{2}-3 \cos 20^{\circ}$

Solution

$\begin{aligned} & 4 \cos ^3 20^{\circ}=\cos \left(3 \times 20^{\circ}\right)+3 \cos 20^{\circ}\left[\because 4 \cos ^3 \theta=\cos 3 \theta+3 \cos \theta\right] \\ & \Rightarrow 4 \cos ^3 20^{\circ}=\cos 60^{\circ}+3 \cos 20^{\circ}=\frac{1}{2}+3 \cos 20^{\circ}\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 2)

Practice more Trigonometric Functions questions on Aicharya