Answer:
=Sin3x+sin2x-sinx
= (sin3x- sinx)+sin2x
= ( 2cos(3x+x)/2 . sin(3x-x)/2 ) + sin2x
= 2cos2xsinx +sin2x
= 2cos2xsinx + 2sinxcosx
= 2sinx (cos2x + cosx )
= 2sinx (2cos(2x+x)/2 . cos(2x-x)/2 )
= 4sinxcos(x/2) cos(3x/2)
Using the formula,
sinA – sinB = 2cos(A+B)/2 . sin(A-B)/2
cosA + cosB = 2cos(A+B)/2 . cos(A-B)/2