Question

Решите уравнение!!!Очень сложное!Или подскажите, как решать) 

Answer 1

$cos^47x - sin^47x = sin2x\\ (cos^27x - sin^27x)(cos^27x + sin^27x) = sin2x\\ cos^27x - sin^27x = sin2x\\ cos^27x - (1 - cos^27x) = sin2x\\ 2cos^2 7x - 1 = sin2x\\ cos14x - sin2x = 0\\ cos(8x + 6x) - sin(8x - 6x) = 0\\ cos8xcos6x - sin8xsin6x - (sin8xcos6x - cos8xsin6x) = 0\\ cos8x(cos6x + sin6x) - sin8x(sin6x + cos6x) = 0\\ (cos6x + sin6x)(cos8x - sin8x) = 0\\ cos6x + sin6x = 0$

$sqrt{2}sin(frac{pi}{4} + 6x) = 0\\ sin(frac{pi}{4} + 6x) = 0\\ frac{pi}{4} + 6x = pi n, n in Z\\ 6x = pi n - frac{pi}{4}, n in Z\\ boxed{x = frac{pi n}{6}- frac{pi}{24}, n in Z}\\ cos8x - sin8x = 0\\ sqrt{2}sin(frac{pi}{4} - 8x) = 0\\ sin(frac{pi}{4} - 8x) = 0\\ frac{pi}{4} - 8x = pi n, n in Z\\ -8x = pi n - frac{pi}{4}, n in Z\\ boxed{x = -frac{pi n}{8}+ frac{pi}{32}, n in Z}$

Answer 2

Спасибо Вам огромное))))