Доказать тождество Cos2a= 1-tg^2a/1+tg^2a

[latex] \frac{1-tg^2a}{1+tg^2a}= \frac{1- \frac{sin^2a}{cos^2a} }{1+ \frac{sin^2a}{cos^2a} }= \frac{ \frac{cos^2a-sin^2a}{cos^2a} }{ \frac{cos^2a+sin^2a}{cos^2a} } = \\ \\ = \frac{cos^2a-sin^2a}{cos^2a}* \frac{cos^2a}{1}=cos^2a-sin^2a=cos2a [/latex]