Question

Find all solutions of the equation in the interval [0, 2pi)
cos^3x=cosx

Answer 1

move cosx to the left side
cos^3x - cosx = 0
factor out a cosx
cosx(cos^2(x) - 1) = 0

cos^2x - 1 = sin^2(x)
and get

cosx(sin^2(x)) = 0

so
cos(x) = 0 and sin^2(x) = 0
cos(x) is 0 at pi/2 and 3pi/2

and sin^2(x) is 0
when x = 0, and x = pi

Answer 2

Thanks so much, very helpful and easy to understand. :)

Answer 3

np glad to help