Question

упростите sin^2x-tg2actg2a sin^2a+sin^2acos^2a+cos^2a

Answer 1

$sin^2x-tg2xcdot ctg2x=sin^2x-1=-(1-sin^2x)=-cos^2x \\\sin^2a+sin^2acdot cos^2a+cos^2a= (sin^2a+cos^2a)+(sinacdot cosa)^2=\\=1+(frac{1}{2}sin2a)^2=1+frac{1}{4}cdot sin^22a$