Exercise 5.2.4 solution
\(\begin{eqnarray*} \cos\left(\frac{\pi}{2}-A\right)\sec A&=&\sin A\sec A\\ &=&\sin A\cdot\dfrac{1}{\cos A}\\ &=&\tan A\\ &=&\cot\left(\frac{\pi}{2}-A\right) \end{eqnarray*}\)