Question

Спростити вираз (sin^[2]x-sin2x+3cos^[2]x)/cos^[2]x

Answer 1

$frac{sin^2x-sin2x+3cos^2x}{cos^2x}= frac{sin^2x-2sinxcosx+3cos^2x}{cos^2x}= \ \ =frac{sin^2x}{cos^2x}-frac{2sinxcosx}{cos^2x}+frac{3cos^2x}{cos^2x}=tg^2x- frac{2sinx}{cosx} +3= \ \ =tg^2x-2tgx+3$