Prove that ( sin 3x / sin x ) - ( cos 3x / cos x ) = 2

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