Question

Докажите торжество а) 1-cos2x/ 1+cos2x =tg^2x

Answer 1

$\displaystyle \frac{1-\cos2x}{1+\cos2x}= \frac{1-(1-2\sin^2x)}{1+(2\cos^2x-1)} = \frac{1-1+2\sin^2x}{1+2\cos^2x-1}= \frac{2\sin^2x}{2\cos^2x} =tg^2x$