Question

Simplify \(\frac{cos^{2}a-cot^{2}a +1}{sin^{2}a + tan^{2} a -1}\)

Answer 1

\[\frac{\cos ^2(\alpha )-\cot ^2(\alpha )+1}{\sin ^2(\alpha )+\tan ^2(\alpha )-1}=-\frac{\cot ^2(\alpha ) \left(-\cos ^2(\alpha )+\cot ^2(\alpha )-1\right)}{\cos ^2(\alpha )-\cot ^2(\alpha )+1}=\cot ^2(\alpha ) \]