Here's two identities you will need:
#sin(theta-α)= sintheta*cosα-costheta*sinα#
#sin^2α+cos^2α=1#
Start:
#sin(180°-α)=(1-cos^2α)/sinα#
#sin(180°)*cosα-cos(180°)*sinα=(1-cos^2α)/sinα#
#cancel((0)*cosα)-(-1)*sinα=(1-cos^2α)/sinα#
#sinα=(1-cos^2α)/sinα#
#sin^2α/sinα=(1-cos^2α)/sinα#
#(sin^2α+1-1)/sinα=(1-cos^2α)/sinα#
Substitute in: #sin^2α+cos^2α# for #1#:
#(sin^2α+1-(sin^2α+cos^2α))/sinα=(1-cos^2α)/sinα#
#((cancel(sin^2α)+1cancel(-sin^2α)-cos^2α))/sinα=(1-cos^2α)/sinα#
#(1-cos^2α)/sinα=(1-cos^2α)/sinα#