11)2cos^2 4x + 3(1 - cos^2 4x) + 2cos 4x = 0
2cos^2 4x + 3 - 3cos^2 4x + 2cos 4x = 0
-cos^2 4x + 2cos 4x + 3 = 0
cos^2 4x - 2cos 4x - 3 = 0
пусть cos 4x = t, |t| <= 1<br> t^2 - 2t - 3 = 0
D = 4 + 12 = 16
t1 = -1; t2 = 3 - не удовл условию
cos 4x = -1
4x = пи + 2пиk
x = пи/4 + пиk/2
Это ответ.
12)8sin^2 5x + 6cos 5x - 3 = 0
8(1 - cos^2 5x) + 6cos 5x - 3 = 0
8 - 8cos^2 5x + 6cos 5x - 3 = 0
-8cos^2 5x + 6cos 5x + 5 = 0
8cos^2 5x - 6cos 5x - 5 = 0
пусть cos 5x = t, |t| <= 1<br> 8t^2 - 6t - 5 = 0
D = 36 + 160 = 196
t1 = (6 - 14) / 16 = -8/16 = -1/2
t2 = (6 + 14) / 16 = 20/16 > 1 - не подходит
cos 5x = -1/2
5x = +-2пи/3 + 2пиk
x = 2пи/15 + 2пиk/5
это ответ.