Well how you can prove this answer is:
sin3xsinx−cos3xcosx=2 TRUE, it is an identity
sin3xsinx−cos3xcosx=2
sin(2x+x)sinx−cos(2x+x)cosx=2
sin2x⋅cosx+cos2x⋅sinxsinx−cos2x⋅cosx−sin2x⋅sinxcosx=2
sin2x⋅cosxsinx+cos2x⋅sinxsinx−cos2x⋅cosxcosx+sin2x⋅sinxcosx=2
sin2x⋅cosxsinx+cos2x⋅sinxsinx−cos2x⋅cosxcosx+sin2x⋅sinxcosx=2
sin2x⋅cosxsinx+cos2x−cos2x+sin2x⋅sinxcosx=2
sin2x⋅cosxsinx+sin2x⋅sinxcosx=2
2⋅sinx⋅cosx⋅cosxsinx+2⋅sinx⋅cosx⋅sinxcosx=2
2⋅sinx⋅cosx⋅cosxsinx+2⋅sinx⋅cosx⋅sinxcosx=2
(2⋅cosx⋅cosx)+(2⋅sinx⋅sinx)=2
2⋅cos2x+2⋅sin2x=2
2⋅(cos2x+sin2x)=2
2⋅(1)=2
2=2 it is an Identity
Hoped I Helped
