Trigonometry Examples

$\sin (A) = \frac{2 m n}{m^{2} - n^{2}}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = n$ .

$\sin (A) = \frac{2 m n}{(m + n) (m - n)}$

Step 2

Take the inverse sine of both sides of the equation to extract $A$ from inside the sine.

$A = \arcsin (\frac{2 m n}{(m + n) (m - n)})$