Question

Спростіть вираз (2tg^2a/1-cos2a)- 1/ctg^2a

Answer 1

$frac{2tg^2x}{1-cos2x}-frac{1}{ctg^2x}=frac{2sin^2x}{cos^2xcdot 2sin^2x}-frac{sin^2x}{cos^2x}=frac{1}{cos^2x}-frac{sin^2x}{cos^2x}=\\= frac{1-sin^2x}{cos^2x}= frac{cos^2x}{cos^2x}=1\\\P.S.quad sin^2x=frac{1-cos2x}{2}quad to quad 1-cos2x=2sin^2x$