Question 232731
1-(cosB-sinB)^2=sin2B


L.H.S
1-(cos^2B-2sinBcosB + sin^2B)
1-cos^2B + 2sinBcosB -sin ^2B


by using sinB+cosB=1 
and 2sinBcosB=sin2B (double angle)


sinB + sin2B - sin^2B
= sin2B (proven)