Chapter 7.5, Problem 35SB

In Problems 35-40, find the exact value of each of the following under the given conditions:

(a) $\sin \left(\alpha \text{ + }\beta \right)$

(b) $\cos \left(\alpha \text{ + }\beta \right)$

(c) $\sin \left(\alpha -\beta \right)$

(d) $\tan \left(\alpha -\beta \right)$

$\sin \alpha \text{ = }\frac{3}{5},0\text{ < }\alpha \text{ < }\frac{\pi }{2};\cos \beta \text{ = }\frac{2\sqrt{5}}{5},-\frac{\pi }{2}\text{ < }\beta \text{ < 0}$