# Does cos240=(cos120)^2-(sin120)^2?

Oct 21, 2016

Yes

Oct 22, 2016

Yes, it does

#### Explanation:

A common trigonometric identity states that

$\cos \left(2 \theta\right) = {\cos}^{2} \left(\theta\right) - {\sin}^{2} \left(\theta\right)$ for any angle $\theta$.

This can be derived from the sum of angles formula

$\cos \left(\alpha + \beta\right) = \cos \left(\alpha\right) \cos \left(\beta\right) - \sin \left(\alpha\right) \sin \left(\beta\right)$

by setting $\alpha = \beta$.

In the given case, that gives us

${\cos}^{2} \left(120\right) - {\sin}^{2} \left(120\right) = \cos \left(2 \cdot 120\right) = \cos \left(240\right)$