# If x is an acute angle, and cos x =4/5, then cos (2 x) is equal to?

Apr 28, 2018

$\cos 2 x = \frac{7}{25}$

#### Explanation:

Use trig identity:
$\cos 2 x = 2 {\cos}^{2} x - 1$
In this case:
$\cos 2 x = \left(2\right) \left(\frac{16}{25}\right) - 1 = \frac{32}{25} - \frac{25}{25} = \frac{7}{25}$
To find the sign of cos 2x, use calculator to approximately get the value of x and 2x.
$\cos x = \frac{4}{5}$ --> $x = {36}^{\circ} 87$ --> $2 x = {73}^{\circ} 74$.
Since 2x is in Quadrant 1, then, cos 2x is positive.
$\cos 2 x = \frac{7}{25}$