# How do you simplify cos(sin^-1(3/5)-cos^-1(1/2))?

May 13, 2016

$\left(\frac{1}{10}\right) \left(\pm 4 \pm 3 \sqrt{3}\right)$

#### Explanation:

Let $a = {\sin}^{- 1} \left(\frac{3}{5}\right) \mathmr{and} b = {\cos}^{- 1} \left(\frac{1}{2}\right)$.

Then, $\sin a = \frac{3}{5} , \cos a = \pm \frac{4}{5} , \cos b = \frac{1}{2} \mathmr{and} \sin b = \pm \frac{\sqrt{3}}{2}$

Now, the given expression is $\cos \left(a - b\right)$

$= \cos a \cos b + \sin a \sin b$

$= \pm \frac{2}{5} \pm 3 \frac{\sqrt{3}}{10} = \left(\frac{1}{10}\right) \left(\pm 4 \pm 3 \sqrt{3}\right)$.

The choice of sign depends on the specified ranges (if any ), for the inverse angles.a and b.