Find all x that satisfy the given equations for 0 less than

Find all x that satisfy the given equations for 0 less than not equal to x less than 2 phi.

For all equations solution for:0<=x <=2pi

6. (cos^2x -4)/(cosx -2) =1

cos^2x -4 = cosx -2

cos^2x - cosx -4 +2 =0

solve the quadratic equation:

cos^2x -2cosx +cosx -2 =0

cosx( cosx -2) + 1( cosx -2) =0

(cosx +1)(cosx -2) =0

cosx =2 .Neglect the solution

cosx =-1

x = pi is the solution

10 ) sqrt3 secx*cscx = 2cscx

sqrt3 secx*cscx - 2cscx =0

cscx( sqrt3secx -2) =0

cscx =0 --->No solutions

sqrt3secx =2 ----> sqrt3/cosx =2

cosx = sqrt3/2 ---> x= cos^-1(sqrt3/2)

x = pi/6 , 2pi-pi/6 = pi/6 , 11pi/6 are the solutions

11. 4tan^2x -1 = tan^2x

3tan^2x -1 =0\'

(sqrt3 tanx +1)(sqrt3 tanx -1) =0

tanx = -1/sqrt3 ---> x =pi -pi/6 , 2pi-pi/6 = 5pi/6 , 11pi/6 ( tan is -ve in IInd and IVrth quadrant)

tanx = 1/sqrt3 ----> x = pi/6 , pi+pi/6 = pi/6 , 7pi/6 ( tan is +ve in Ist and IIIrd quadrant)

x =pi/6, 5pi/6 , 7pi/6, 11pi/6 are the solutions