Trigonometry Examples

$\sin (x) \cos (y) = \frac{1}{2} \cdot (\sin (x + y) + \cos (x - y))$

Step 1

Simplify $\frac{1}{2} \cdot (\sin (x + y) + \cos (x - y))$ .

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Step 1.1

Apply the distributive property.

$\sin (x) \cos (y) = \frac{1}{2} \sin (x + y) + \frac{1}{2} \cos (x - y)$

Step 1.2

Combine $\frac{1}{2}$ and $\sin (x + y)$ .

$\sin (x) \cos (y) = \frac{\sin (x + y)}{2} + \frac{1}{2} \cos (x - y)$

Step 1.3

Combine $\frac{1}{2}$ and $\cos (x - y)$ .

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

Step 1.4

Combine the numerators over the common denominator.

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