Can anyone help me verify these two identities

1. csc2x= 1/2 secx cscx I am not sure how to start this one

My second one I am not sure if I have done it right?

(sinx+cosx)^2-1= sin2x

(sinx+cosx) (sinx+cosx)-1

sinx^2+sinxcosx+sinxcosx+cosx^2-1

1+2sincosx-1=sin2x

2sinxcosx=sin2x

sin2x=sin2x Did I do this right?