Trigonometry Examples

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

Step 1

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $\cos^{2} (x)$ from both sides of the equation.

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

Step 1.2

Add $\sin^{2} (y)$ to both sides of the equation.

$\cos (x - y) \cos (x + y) - \cos^{2} (x) + \sin^{2} (y) = 0$

Step 2

Replace $\sin^{2} (y)$ with $1 - \cos^{2} (y)$ .

$\cos (x - y) \cos (x + y) - \cos^{2} (x) (1 - \cos^{2} (y)) = 0$

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

Apply pythagorean identity.

$\cos (x - y) \cos (x + y) - \cos^{2} (x) \sin^{2} (y) = 0$