4sin3x+cos3x=4

Question

4sin3x+cos3x=4

Answer 1

2(cos4x - sinx*cos3x) = sin4x + sin2x 
2*cos4x - sin4x + sin2x = sin4x + sin2x (*) 
cos4x - sin4x = 0 
cos4x = sin4x 
4x = Pi/4 + Pi*k 
x = Pi/8 + Pi/4 * k