Question

How do you verify the trigonometry expression cscx-1=1-sinx/sinx

Answer 1

cscx = 1/sinx 
So substitute cscx for 1/sinx
1/sinx - 1
1 can be written in terms of sinx
1 = sinx/sinx (anything over itself is 1)
1/sinx - sinx/sinx = (1 - sinx)/sinx