\[\frac{1 - \left( \sin a + \cos a \right)^{2}\ }{\sin a \bullet \cos a - ctg\ a} = 2\ tg^{2}\text{\ a}\]
\[2 \bullet \frac{\sin^{2}a}{1 - \sin^{2}a} = 2\ tg^{2}\text{\ a}\]
\[2 \bullet \frac{\sin^{2}a}{\cos^{2}a} = 2\ tg^{2}\text{\ a}\]
\[2\ tg^{2}\ a = 2\ tg^{2}\text{\ a}.\]
\[Что\ и\ требовалось\ докзать.\]