SOLUTION: can someone help me with this please thank you.solve the equation in [0,2pi] using any appropriate method.answer in exact form. 10tan(pi/2-x)sin^2x=5sqrt3/2

First thing you need to know and to apply is   = cot(x) = .


When you apply it, your equation becomes


 = ,   or

 = .


Second thing you need to know is  2*cos(x)*sin(x) = sin(2x).


When you apply it, the last equation becomes


sin(2x) = .


It has the solutions  2x = ,  2x = ,  2x =   and  2x = .


Therefore, the solutions for x are  ,  ,    and  .