Solve the equation 2 sin 2x cos 2x sin 2x 2 cos 2x l 0 f

Solve the equation 2 sin 2x cos 2x - sin 2x + 2 cos 2x - l = 0 for the exact values of x, where, 0 lessthanorequalto x lessthanorequalto 2pi

2sin2xcos2x- sin2x +2cos2x -1 =0

sin2x (2cos2x -1) +( 2cos2x -1) =0

(sin2x +1)(2cos2x -1) =0

sin2x =-1

Gene solution : 2x = pi+pi/4 +2kpi

x = 5pi/8 + k*pi

2x = 2pi -pi/4 +2kpi

x= 7pi/8 +k*pi

a) for 0<=x< 2pi

x = 5pi/8 , 13pi/8 , 7pi/8 , 15pi/8

b) for x belonging to Real

X = 5pi/8 + k*pi, 7pi/8 +k*pi