(sin^2(a)-cos^2(a)) ^2 +2cos^2(a)*sin^2(a)=sin^4(а)+cos^4(a) Докажите тождество

Question

(sin^2(a)-cos^2(a)) ^2 +2cos^2(a)*sin^2(a)=sin^4(а)+cos^4(a)
Докажите тождество

Answer 1

(sin²a-cos²a)+2cos²a*sin²a=sin^4a-2sin²a*cos²a+cos^4a+2cos²a*sin²a=
=sin^4a+cos^4a