Question

find all solutions of the given equation in the interval [0,2pi]
cosx=cos3x

Answer 1

\[\pi\] would work

Answer 2

i guess 0 would work as well. and maybe
\[\frac{\pi}{2}\]

Answer 3

maybe write 4cos^3(x) - 3cos(x) = cos(3x) (as this is an identity i think (correct me if i am wrong)
Then obviously: cos(x) = 4cos^3(x) - 3cos(x) hence 0 = 4cos(x)(cos^2(x) - 1) so you can tell right away that all the places where cos(x) vanishes in that interval are solutions. Next solve cos^2(x) -1 = 0 for x to find the others

Answer 4

@Callum, yes, that is the correct identity. This is how I would do the problem.