Answer:
x = 0 and 2pi/3
Explanation
Given the expression
cos(2x)=cos(x)
In trigonometry expression;
cos2x = 2xos^2x - 1
Substituting into the equation given;
cos(2x)=cos(x)
2xos^2x - 1 = cos x
Rearrange
2xos^2x - 1 - cosx - 1 = 0
Let P = cosx
2P^2 - P - 1 = 0
Factorize
2P^2 - 2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P+1 = 0 and P-1 = 0
P = -1/2 and 1
Recall that P = cosx
-1/2 = cosx
x = cos^-1(-1/2)
x = 120 degrees = 2pi/3
If P = 1
cosx = 1
x = cos^-1(1)
x = 0
Hence the value of x that satisfies the equation is 0 ad 2pi/3
