Verify the identity: sin^1/2x cosx - sin^5/2x cosx = cos^3x √sinx

Help with this problem, please!!!!

okay for sin^5/2x you can split that up into sin^1/2x*sin^2x


sin^1/2xcosx-sin^1/2x*sin^2xcosx

now you can factor out a sin^1/2xcosx

sin^1/2xcosx(1-sin^2x)

remember identites: sin^2x+cos^2x=1 so 1-sin^2x=cos^2x

sin^1/2xcosx(cos^2x)

now multiply everything out

sin^1/2xcos^3x.

YOu'll find out that factoring when you are trying to verify an identity becomes very helpful because it helps simplifies the problem down to something that you can recognize.

sin^1/2x cosx - sin^5/2x cosx
= sin^1/2x cosx (1-sin^2x)
= sin^1/2x cosx cos^2x
= cos^3x √sinx