Solve the following equation on the interval 02pi cosx2sinxc

Solve the following equation on the interval [0,2pi]

cosx+2sinxcosx=0

The solution set is: { }

Solution

cos x + 2sinx cos x=0

cos x(1+2 sin x)=0

cos x=0                    1 + 2sinx =0

x= cos^-10                        sin x= -1/2

x= pi/2, 3pi/2                        x= sin^-1(-1/2) = 7pi/6, 11pi/6

x= pi/2, 7pi/6, 3pi/2, 11pi/6

solution set is {pi/2, 7pi/6, 3pi/2, 11pi/6}