1-sin8a/2sin2acos2a-2cos^(2)2a+1

Упростим выражение.

(1 sin (8 * a))/(2 * sin (2 * a) * cos (2 * a) 2 * cos^2 (2 * a) + 1);

Применим формулы приведения.

(1 sin (8 * a))/(sin (2 * 2 * a) 2 * cos^2 (2 * a) + 1);

(1 sin (8 * a))/(sin (4 * a) 2 * cos^2 (2 * a) + 1);

(1 sin (8 * a))/(sin (4 * a) 2 * cos^2 (2 * a) + cos^2 (2 * a) + sin^2 (2 * a));

Приведем сходственные.

(1 sin (8 * a))/(sin (4 * a)   cos^2 (2 * a) + sin^2 (2 * a));

(1 sin (8 * a))/(sin (4 * a)   (cos^2 (2 * a) - sin^2 (2 * a))); 

(1 sin (8 * a))/(sin (4 * a) cos^2 (2 * 2 * a)); 

(1 sin (8 * a))/(sin (4 * a) cos^2 (4 * a)); 

(1 2 * sin (4 * a) * cos (4 * a))/((sin (4 * a) cos (4 * a)) * (sin (4 * a) + cos (4 * a));

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

(sin (4 * a) cos (4 * a))/(sin (4 * a) + cos (4 * a)).