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 \frac{1-tan^2A}{1+tan^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+sin^2A}}\\\\ = \frac{cos^2A-sin^2A}{1} \\\\=cos^2A-sin^2A
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