# How do you simplify 4 sin 21 cos 21?

Nov 23, 2015

$4 \sin \left({21}^{\circ}\right) \cos \left({21}^{\circ}\right) = 2 \sin \left({42}^{\circ}\right) \approx 1.328$

#### Explanation:

Double angle formula for sine function:
$\textcolor{w h i t e}{\text{XXX}} 2 \sin \left(\theta\right) \cos \left(\theta\right) = \sin \left(2 \theta\right)$

$4 \sin \left({21}^{\circ}\right) \left(\cos \left({21}^{\circ}\right)\right) = 2 \left(\sin \left(2 \times {21}^{\circ}\right)\right) = 2 \sin \left({42}^{\circ}\right)$

Using a calculator:
$\textcolor{w h i t e}{\text{XXX}} 2 \sin \left({42}^{\circ}\right) = 1.328$