solve the following equations for all values of the angle ov

solve the following equations for all values of the angle over 0<x<2pi give exact solutions

Solution

4sin^2x -3 =0

sin^2x = 3/4

sinx = sqrt(3)/2 , -sqrt(3)/2

sin is +ve in Ist and IInd quadrant.

sin is -ve in IIIrd and IVrth quadrant

sinx = sqrt(3)/2

x = sin^-1(sqrt3/2)

x = pi/3 , pi-pi/3 = pi/3 , 2pi/3

sinx = -sqrt(3)/2

x = pi +pi/3 , 2pi -pi/3

= 4pi/3 , 5pi/3

Solution : x = pi/3 , 2pi/3 , 4pi/3 , 5pi/3 in the interval 0<x<2pi