tg^2a-1/tg^2a+1 +cos^2a

Решите задачу:

$\mathtt{\frac{tg^2a-1}{tg^2a+1}+cos^2a=\frac{\frac{sin^2a}{cos^2a}-1}{\frac{sin^2a}{cos^2a}+1}+cos^2a=\frac{\frac{sin^2a}{cos^2a}-\frac{cos^2a}{cos^2a}}{\frac{sin^2a}{cos^2a}+\frac{cos^2a}{cos^2a}}+cos^2a=\frac{\frac{sin^2a-cos^2a}{cos^2a}}{\frac{sin^2a+cos^2a}{cos^2a}}+}\\\mathtt{cos^2a=\frac{sin^2a-cos^2a}{sin^2a+cos^2a}+cos^2a=sin^2a-cos^2a+cos^2a=sin^2a}$