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

May 19, 2016

$0 , \pm \frac{24}{25}$.

#### Explanation:

Let $a = {\sin}^{- 1} \left(- \frac{3}{5}\right)$.

Then, $\sin a = - \frac{3}{5} < 0$. So, a is in the 3rd quadrant or in the 4th.

Accordingly,

cos a = (- or +)(4/5).

Let $b = {\cos}^{- 1} \left(\frac{3}{5}\right)$.

Then, $\cos b = \frac{3}{5} > 0.$ So, b is in the 1st quadrant or in the 4th.

Accordingly, sin b = +- 4/5.

Now, the given expression$= cos ( a + b ) = cos a cos b - sin a sin b $= \left(- \mathmr{and} +\right) \left(\frac{4}{5}\right) \left(\frac{3}{5}\right) - \left(- \frac{3}{5}\right) \left(\pm \frac{4}{5}\right)$$= \left(- \mathmr{and} +\right) \left(\frac{12}{25}\right) \pm \frac{12}{25}$$= 0 , \pm \frac{24}{25}\$