Вычислите:
(Sin^2 a- cos^2 a)^2+4sin^2 a cos^2 a

(Sin^2 a- cos^2 a)^2+4sin^2 a cos^2 a ==sin^4a-2sin^2acos^2a+cos^4a+4sin^2acos^2a==sin^4a+2sin^2acos^2a+cos^4a=(sin^2a+cos^2a)^2=1

=sin⁴(α)-2*sin²(α)*cos²(α)+cos⁴(α)+4*sin²(α)*cos²(α)=sin⁴(α)+2*sin²(α)*cos²(α)+cos⁴(α)=(sin²(α)+cos²(α))²=1²=1. Ответ: 1.