(2sin2a-cos2a)²+(2cos2a+sin2a)²

Упростим выражение (2 * sin (2 * a) - cos (2 * a))^2 + (2 * cos (2 * a) + sin (2 * a))^2. 

(2 * sin (2 * a))^2 - 2 * 2 * sin (2 * a) * cos (2 * a) + cos^2 (2 * a) + (2 * cos (2 * a))^2 + 2 * 2 * cos (2 * a) * sin (2 * a) + sin^2 (2 * a); 

4 * sin^2 (2 * a) - 4 * sin (2 * a) * cos (2 * a) + cos^2 (2 * a) + 4 * cos^2 (2 * a) + 4 * sin (2 * a) * cos (2 * a) + sin^2 (2 * a); 

4 * sin^2 (2 * a)  + cos^2 (2 * a) + 4 * cos^2 (2 * a) + sin^2 (2 * a);  

4 * (sin^2 (2 * a) + cos^2 (2 * a)) + (cos^2 (2 * a) + sin^2 (2 * a)) = 4 * 1 + 1 = 4 + 1 = 5. 

Ответ: 5.