Решите уравнение f' (x) = 0, если f (x) = cos^3x-sin^3x

F' (x) = 3cos^2 (x) * (-sin (x)) - 3sin^2 (x) * cos (x) = - 3 (cos^2 (x) sinx+sin^2 (x) cosx)

-3 (cos^2 (x) sinx+sin^2 (x) cosx) = 0

cos^2 (x) sinx+sin^2 (x) cosx=0

sinxcosx (cosx+sinx) = 0

sinxcosx=0

sinx=0

x=pi*n, n∈Z

cosx=0

x=pi/2+pi*k, k∈Z

sinx = - cosx |:cosx≠0

tgx = - 1

x = - pi/4+pi*t, t∈Z