# What does cosx sinx equal?

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Mar 7, 2016

$\cos \left(x\right) \sin \left(x\right) = \sin \frac{2 x}{2}$

#### Explanation:

So we have

$\cos \left(x\right) \sin \left(x\right)$

If we multiply it by two we have

$2 \cos \left(x\right) \sin \left(x\right)$

Which we can say it's a sum

$\cos \left(x\right) \sin \left(x\right) + \sin \left(x\right) \cos \left(x\right)$

Which is the double angle formula of the sine

$\cos \left(x\right) \sin \left(x\right) + \sin \left(x\right) \cos \left(x\right) = \sin \left(2 x\right)$

But since we multiplied by 2 early on to get to that, we need to divide by two to make the equality, so

$\cos \left(x\right) \sin \left(x\right) = \sin \frac{2 x}{2}$

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