I am trying to figure out with [0,2pie) find solutions for tan(x/2)=cot(x).

Question

I am trying to figure out with [0,2pie) find solutions for tan(x/2)=cot(x).

Answer 1

tan(x/2) = (1 - cosx) / sinx

 

So, if tan(x/2) = cotx. then (1 - cosx) / sinx = cosx / sinx

 

Therefore, 1 - cosx = cosx

 

                   2cosx = 1

 

                     cosx = 1/2     x = π/3 or 5π/3