32sinx = cosx
32sinx/cosx = cosx/cosx
32tgx = 1
tgx = 1/32
x = arctg1/32 + πk, k€Z.
cos²x + 7cosx = 8
Пусть t = cosx ( t€[-1; 1]
t² + 7t = 8
t² + 7t - 8 = 0
t1 + t2 = -7
t1•t2 = -8
t1 = 1
t2 = -8 - не уд. условию
Обратная замена:
cosx = 1
x = 2πk, k€Z.