What is the general solution of the equation cosx +3sinx +sin3x -cos3x=0 ?

Simply substitute sin3x=3s-4s^3, s being sinx and cos3x= 4c^3-3c, c being cosx. Then use the identity c^3+s^3= (c+s)(1-sc) and simplify. You will then get two conditions- either sinx=0 or -1= 2sc+2c^2

But the latter is not possible since the LHS in it is equal to sin2x+cos2x+1 whose minimum value is greater than -1. Hence sinx= 0 or x= nπ is the complete solution