Find all solutions of the equation in the interval [0, 2𝜋). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 50 sin^2(x)=50+25cos(x)

Question

50sin^2x=50+25cos(x)

50(1-cos2x/2)=50+25cos(x)

25-25cos2x=50+25cos(x)

0=25cos(2x)+25cos(x)+25

0=50cos3x+25

-25=50cos(3x)

-1/2=cos(3x)

I'm not sure what to do from here

Answer 1

What angle(s) have a cosine of -1/2?

Then divide those angles by 3.