Question

verify algebraically these two equations are equivalent: (sinx+sin3x)2sin2x = cosx

Answer 1

Sorry, (sinx+sin3x)/(2sin2x) = cosx

Answer 2

(sinx + sin(2x + x)) = 2(cosx)sin2x
sinx + sin2xcosx + cos2xsinx = 2cosxsin2x
sinx + cos2xsinx = cosxsin2x
cos2x = (cosx)^2 - (sinx)^2 <- identity
sin2x = 2sinxcosx <- identity
sinx + sinx(cosx)^2 - (sinx)^3 = 2sinx(cosx)^2
1 + (cosx)^2 - (sinx)^2 = 2(cosx)^2
1-(sinx)^2 = (cosx)^2 <- identity
so :
(cosx)^2 + (cosx)^2 = 2(cosx)^2

maybe there is a shorter way

Answer 3

Thank You So Much. I'm staring at my double angle identities right now and was just having a hard time make it through line by line.