Step-by-step explanation:
L.H.S=(1-cosB)(1+cosB)
=(1-cos^2B). {using (a+b) (a-b)=(a^2-b^2)in second step}
=sin^2B
=1/cosec^2B
Therefore,L.H.S=R.H.S proved
Angle B=180-(38+31.6)=110.4
by law of sin
sin B/b=sinA/A
sin(110.4)/b=sin38/25
b=25*sin(110.4)/sin(38)=38.06
Hope this helped :)
Check the image below for working
I think it is z I could be wrong