Question

доказать тождество по алгебре

Answer 1

$displaystyle tt sin^3:alpha(1+ctg:alpha)+cos^3:alpha(1+tg:alpha)=sin:alpha+cos:alpha\displaystyle tt sin^3:alpha(1+frac{cos:alpha}{sin:alpha})+cos^3:alpha(1+frac{sin:alpha}{cos:alpha})=sin:alpha+cos:alpha\displaystyle tt sin^3:alphacdotfrac{sin:alpha+cos:alpha}{sin:alpha}+cos^3:alphacdotfrac{cos:alpha+sin:alpha}{cos:alpha}=sin:alpha+cos:alpha$

$displaystyle tt sin^2:alphacdot(sin:alpha+cos:alpha)+cos^2:alphacdot(cos:alpha+sin:alpha)=sin:alpha+cos:alpha\displaystyle tt (sin:alpha+cos:alpha)cdot(sin^2:alpha+cos^2:alpha)=sin:alpha+cos:alpha\displaystyle tt (sin:alpha+cos:alpha)cdot1=sin:alpha+cos:alpha\displaystyle tt sin:alpha+cos:alpha=sin:alpha+cos:alpha$