Question

sinA.cotB.sinB + cotA. sinB. sinA = sin(A + B)

Answer 1

L.H.S. = sinA.cotB.sinB + cotA.sinB.sinA

L.H.S. = sinA.cosB/sinB.sinB + cosA/sinA.sinB.sinA

L.H.S. = sinA.cosB + cosA.sinB

L.H.S. = sin(A+B)

(There's and identity for compound angles, it goes like sin(A+B)= sinA.cosB + cosAsinB)

L.H.S. = R.H.S.

Hence proved.