Algebra Examples

$\cos (x) \cos (y) + \sin (x) \sin (y) + \cos (x) \cos (y) - \sin (x) \sin (y) = 2 \cos (x) \cos (y)$

Step 1

Start on the left side.

$\cos (x) \cos (y) + \sin (x) \sin (y) + \cos (x) \cos (y) - \sin (x) \sin (y)$

Step 2

Simplify.

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Step 2.1

Add $\cos (x) \cos (y)$ and $\cos (x) \cos (y)$ .

$2 \cos (x) \cos (y) + \sin (x) \sin (y) - \sin (x) \sin (y)$

Step 2.2

Subtract $\sin (x) \sin (y)$ from $\sin (x) \sin (y)$ .

$2 \cos (x) \cos (y) + 0$

Step 2.3

Add $2 \cos (x) \cos (y)$ and $0$ .

$2 \cos (x) \cos (y)$

Step 3

Because the two sides have been shown to be equivalent, the equation is an identity.

$\cos (x) \cos (y) + \sin (x) \sin (y) + \cos (x) \cos (y) - \sin (x) \sin (y) = 2 \cos (x) \cos (y)$ is an identity