Question

$\cos A+\cos (240°+A)+\cos (240°-A)=?$

• A. $\cos A$
• B. $0$
• C. $\sqrt{3}\sin A$
• D. $\sqrt{3}\cos A$

Answer 1

The correct option is B

$0$

Explanation for the correct option:

Given, $\cos A+\cos (240°+A)+\cos (240°–A)$

Using the identity $\cos (A+B)+\cos (A–B)=2\cos A\cos B$, we get

$=\cos A+2\cos 240°\cos A$

$=\cos A[1+2\cos (270°–30°\left)\right]$

$=\cos A[1+2(-\sin 30°\left)\right]$ ; $\left[\mathbf{\because }\mathit{c}\mathit{o}\mathit{s}\mathbf{}\left(\frac{3\pi }{2}-\theta \right)\mathbf{=}\mathbf{-}\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\right]$

$=\cos A\left(1–2\times \frac{1}{2}\right)$

$=\cos A[1–1]$

$=\mathbf{0}$

Hence, Option ‘B’ is Correct.