5tanx = 2sin2x solve for interval (0 2π)

Question

5tanx = 2sin2x solve for interval (0 2π)
algebraic means without calculator

Answer 1

5tanx=2sin2x

5tanx-2sin2x=0

5sinx/cosx-2(2sinxcosx)=0

5sinx/cosx-4sinxcosx=0

sinx(5/cosx-4cosx)=0

sinx=0

on the unit circle x=0º or x=180º

5/cosx-4cosx=0

5/cosx=4cosx

5/4=cos²x

cosx=±√(5/4)

cosx=±√5/2=±1.118034 which is out of the range of cos

-1<cos<1

x=0º or x=180º