Question

sin^3x(1+ctgx)+cos^3x(1+tgx)=sinx+cosx доказать тождество

Answer 1

$sin^3x(1+ctgx)+cos^3x(1+tgx)=\ sin^3x+sin^2xcosx+cos^3x+cos^2xsinx=\ (sin^2xcosx+cos^3x)+(cos^2xsinx+sin^3x)=\ cosx(sin^2x+cos^2x)+sinx(sin^2x+cos^2x)=cosx+sinx$