Sin^4 a + cos^4 a - sin^6 a - cos^6 a = (sin^2 * 2a)/4 Сгруппируем (sin^4 a - sin^6 a) + (cos^4 a - cos^6 a) = (sin^2 2a)/4 применив тождества 1- sin ^2 a = cos^2 a 1 - cos^2 a = sin^2 a имеем sin^4 a (1 – sin^2 a) + cos^4 a (1- cos^2 a) = (sin^2 * 2a)/4 sin^4 a * cos^2 a + cos^4 a * sin^2 a = (sin^2 * 2a)/4 sin^2 a * cos^2 a (sin^2 a + cos^2 a) = (sin^2 * 2a)/4 (4 *sin^2 a * cos^2 a)/4 = (sin^2 * 2a)/4 (sin^2 *2 a)/4 = (sin^2 * 2a)/4
Сгруппируем
(sin^4 a - sin^6 a) + (cos^4 a - cos^6 a) = (sin^2 2a)/4
применив тождества 1- sin ^2 a = cos^2 a
1 - cos^2 a = sin^2 a
имеем
sin^4 a (1 – sin^2 a) + cos^4 a (1- cos^2 a) = (sin^2 * 2a)/4
sin^4 a * cos^2 a + cos^4 a * sin^2 a = (sin^2 * 2a)/4
sin^2 a * cos^2 a (sin^2 a + cos^2 a) = (sin^2 * 2a)/4
(4 *sin^2 a * cos^2 a)/4 = (sin^2 * 2a)/4
(sin^2 *2 a)/4 = (sin^2 * 2a)/4