$\displaystyle \begin{array}{{>{\displaystyle}l}} P=\frac{1-cosa}{sina} .\frac{( 1+cosa)^{2}}{sin^{2} a-1}\\ =\frac{1-cos^{2} a}{sina} .\frac{( 1+cosa)}{sin^{2} a-1}\\ =\frac{sin^{2} a}{sina} .\frac{1+cosa}{-cos^{2} a}\\ =\frac{sina( 1+cosa)}{-cos^{2} a} \end{array}$