Solve the equation analytically Solve over the interval 0 2p

Solve the equation analytically. Solve over the interval (0, 2pi), giving exact values of solutions and endpoints. sin (x/2) = cos (x/2) The solution set is {}. (Type an exact answer, using x as needed. Use a comma to separate answers as needed.)

Solution

sin(x/2) = cos(x/2)

sin(x/2) - cos(x/2) =0

2cos(x/2+x/2)/2*sin(x/2 - x/2) =0

0 =0

So, solution : x= pi/2 when sinpi/4 = cospi/4 = 1/sqrt2

Solution : x= pi/4