# How do you prove  cos(x+y)cosy + sin(x+y)siny = cosx?

Apr 28, 2016

#### Explanation:

Recall the trigonometrical identity

$\cos \left(A - B\right) = \cos A \cos B + \sin A \sin B$

Putting $A = x + y$ and $B = y$, we get

$\cos \left(x + y - y\right) = \cos \left(x + y\right) \cos y + \sin \left(x + y\right) \sin y$

or transposing LHS to RHS and vice-versa

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