Question

Помогите плиз! Докажите тождество:

Answer 1

$1); frac{sinA+cosAcdot tgA}{cosA+sinAcdot ctgA} = frac{sinA+cosAcdot frac{sinA}{cosA}}{cosA+sinAcdot frac{cosA}{sinA}} = frac{sinA+sinA}{cosA+cosA} =frac{2sinA}{2cosA}=tgA\\2); frac{1}{tg^2A+1} - frac{1}{ctg^2A+1} = frac{1}{frac{1}{cos^2a}} - frac{1}{frac{1}{sin^2A}} = cos^2A-sin^2A=cos2A$