Trigonometry Examples

$\cos (a - B) + \cos (a + B)$

Step 1

Use the difference formula for cosine to simplify the expression. The formula states that $\cos (A - B) = \cos (A) \cos (B) + \sin (A) \sin (B)$ .

$(\cos (a) \cdot \cos (B) + \sin (a) \cdot \sin (B)) + \cos (a + B)$

Step 2

Remove parentheses.

$(\cos (a) \cdot \cos (B) + \sin (a) \cdot \sin (B)) + \cos (a + B)$

Step 3

Multiply $\sin (a)$ by $\sin (B)$ .

$\cos (a) \cos (B) + \sin (a) \sin (B) + \cos (a + B)$

Step 4

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

$\cos (a) \cdot \cos (B) + \sin (a) \cdot (\sin (B) (\cos (B) \cdot \cos (a) - \sin (B) \cdot \sin (a)))$

Step 5

Remove parentheses.

$\cos (a) \cdot \cos (B) + \sin (a) \cdot \sin (B) + \cos (B) \cdot \cos (a) - \sin (B) \cdot \sin (a)$