Question

cos a/1+sina + 1-sina/cosa

Answer 1

$$\begin{array}{l} \frac{\cos a}{(1 + \sin a)} + \frac{(1 + \sin a)}{\cos a} = \frac{\cos^{2} a + (1 + \sin a)^{2}}{\cos a \cdot (1 + \sin a)} = \\ = \frac{\cos^{2} a + 1 + 2 \cdot \sin a + \sin^{2} a}{\cos a \cdot (1 + \sin a)} = \left| \sin^{2} a + \cos^{2} a = 1 \right| = \frac{2 + 2 \cdot \sin a}{\cos a \cdot (1 + \sin a)} = \\ = \frac{2(1 + \sin a)}{\cos a \cdot (1 + \sin a)} = \frac{2}{\cos a}. \end{array}$$

Answer: $\frac{2}{\cos a}$