sinx+cosx⋅sin2x+3cos3x=2.(cos4x+sin3x)
⇔sinx+cosx⋅sin2x+3cos3x=2cos4x+2sin3x
⇔sinx−2sin3x+cosx.sin2x+3cos3x=2cos4x
⇔sinx.(1−2sin2x)+cosx.sin2x+3cos3x=2cos4x
⇔sinx.cos2x+cosx.sin2x+3cos3x=2cos4x
⇔sin.(x+2x)+3cos3x=2cos4x
⇔sin3x+3cos3x=2cos4x
⇔21sin3x+23cos3x=cos4x
⇔cos3π.sin3x+sin3π.cos3x=cos4x
⇔sin.(3x+3π)=sin(xπ−4x)
⇔⎣⎡3x+3π=2π−4x+k2π3x+2π=π−2π+4x+k2π
⇔⎣⎡x=42π+7k2πx=−6π+k2π(k∈Z)