Solve the following inequality Express the exact answer in i

Solve the following inequality. Express the exact answer in interval notation, restricting your attention to -2pi

Solution

sin(2x) >= sinx

Interval -2pi<=x <= 2pi

sin(2x) - sinx > =0

2sinxcosx -sinx>=0

sinx( 2cosx -1) >=0

sinx> =0 and 2cosx -1> =0

x>=0, pi , 2pi, -pi, -2pi

2cosx -1> =0 ---> cosx >= 1/2

x >=pi/3 , 5pi/3 , -pi/3 , -5pi/3

Option C satisfies the solution