Cos x sin x The equation for solution in the interval 0 2 p

Cos x = sin x. The equation for solution in the interval [0, 2 pi] 2 squareroot 3 sin 4x = 3

Solution

2sqrt3 sin4x = 3

Let 4x = u

2sqrt3sinu = 3

sinu = 3/2sqrt(3) = sqrt3/2

u = pi/3 , 2pi/3

4u = pi/3 , 2pi/3

u = (6kpi+ pi)/12 , (3kpi +pi)/6

u = pi/12 , 7pi/12 , 19pi/12 , pi/6 , 2pi/3 , 7pi/6 , 10pi/6   ( solution)