Question

упростить:(sin²a-cos²a)²+2cos²a*sin²a 

Answer 1

$(sin^2a-cos^2a)^2+2cos^2a*sin^2a =sin^4a+cos^4a-2sin^2a*cos^2a+$$+2cos^2a*sin^2a=sin^4a+cos^4a=(sin^2a)^2+(cos^2a)^2=$$=(sin^2a+cos^2a)^2-2sin^2a*cos^2a=1- frac{1}{2}sin^22a$