Question

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

Answer 1

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