Giải phương trình sinx + cosx .sin2x + căn 3 cos 3x = 2(cos4x+sin^3x)

Ta có:

 sinx+cosx.sin2x+3cos3x=2cos4x+sin3x
 ⇔sinx+cosx.sin2x+3cos3x=2cos4x+2sin3x
 ⇔sinx−2sin3x+cosx.sin2x+3cos3x=2cos4x
 ⇔sinx1−2sin2x+cosx.sin2x+3cos3x=2cos4x
 ⇔sinx.cos2x+cosx.sin2x+3cos3x=2cos4x
 ⇔sinx + 2x+3cos3x=2cos4x
 ⇔sin3x+3cos3x=2cos4x
 ⇔12sin3x+32cos3x=cos4x
 ⇔cosπ3.sin3x+sinπ3.cos3x=cos4x
 ⇔sinπ3+3x=sinπ2−4x
 ⇔3x+π3=π2−4x+k2π3x+π2=π−π2+4x+k2π ⇔x=π42+k2π7x=−π6+k2πk∈ℤ