Solve : 2tan3x+cos2x+1=tan3x+2cos2x

Answer 1

kind of messy. First, just rearrange things a bit to get
tan3x + 1 = cos2x
this is clearly true for multiples of 2π, but there are surely other roots
I doubt this will yield to algebraic solution. The resulting attempts at simplification will result in cubic equations, so you better trot out your graphic or numeric methods.
I get other roots as x = 0.78, 1.73, 3.93, 4.87

Answer 2

There is no solution for this question