Chapter 7 - Trigonometry and Periodic Functions - Review Exercises and Problems for Chapter Seven - Page 317: 55

$1-\sin A$

Multiply the numerator and denominator by $1-\sin A$ to get $$\frac{\cos^2 A(1-\sin A)}{(1+\sin A)(1-\sin A)}=\frac{\cos^2 A(1-\sin A)}{1-\sin^2 A}$$ Since $\sin^2 A + \cos^2 A = 1$, $1-\sin^2 A = \cos^2 A$. Therefore, the expression becomes $$\frac{\cos^2 A(1-\sin A)}{\cos^2 A}=1-\sin A$$