Trigonometry Examples

$\sin (A + B) + \sin (A - B)$

Step 1

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

$(\sin (A) \cos (B) + \cos (A) \sin (B)) + \sin (A - B)$

Step 2

Remove parentheses.

$(\sin (A) \cos (B) + \cos (A) \sin (B)) + \sin (A - B)$

Step 3

Remove parentheses.

$\sin (A) \cos (B) + \cos (A) \sin (B) + \sin (A - B)$

Step 4

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

$\sin (A) \cos (B) + \cos (A) \sin (B) (\sin (A) \cos (B) - \cos (A) \sin (B))$

Step 5

Remove parentheses.

$\sin (A) \cos (B) + \cos (A) \sin (B) + \sin (A) \cos (B) - \cos (A) \sin (B)$