# How do you verify the identity (1+siny)(1+sin(-y))=cos^2y?

Jan 17, 2017

see below

#### Explanation:

Left Hand Side:

Use the property for odd trigonometric function: $\sin \left(- y\right) = - \sin y$

$\left(1 + \sin y\right) \left(1 + \sin \left(- y\right)\right) = \left(1 + \sin y\right) \left(1 - \sin y\right)$

$= 1 - {\sin}^{2} y$

Now use the property ${\sin}^{2} y + {\cos}^{2} y = 1$ and solve for ${\cos}^{2} y$

$= {\cos}^{2} y$

$\therefore =$ Right Hand Side