# Question #c1e7d

Dec 13, 2016

#### Explanation:

Verify: ${\left(\sin \left(\theta\right) + \cos \left(\theta\right)\right)}^{2} = 1 + 2 \sin \left(\theta\right) \cos \left(\theta\right)$

I will only make changes to the left side.

Expand the square:

${\sin}^{2} \left(\theta\right) + 2 \sin \left(\theta\right) \cos \left(\theta\right) + {\cos}^{2} \left(\theta\right) = 1 + 2 \sin \left(\theta\right) \cos \left(\theta\right)$

Move the swap the second and third terms:

${\sin}^{2} \left(\theta\right) + {\cos}^{2} \left(\theta\right) + 2 \sin \left(\theta\right) \cos \left(\theta\right) = 1 + 2 \sin \left(\theta\right) \cos \left(\theta\right)$

Use the identity $1 = {\sin}^{2} \left(\theta\right) + {\cos}^{2} \left(\theta\right)$:

$1 + 2 \sin \left(\theta\right) \cos \left(\theta\right) = 1 + 2 \sin \left(\theta\right) \cos \left(\theta\right)$

Verified.