Given that `A=b=45^(@)`.

Now, `sin(A+B)=sin(45^(@)+45^(@))=sin90^(@)=1`.

Also, `sinA cosB +cosA sinB = sin 45^(@) cos 45^(@)+cos45^(@) sin 45^(@)`

`=(1)/(sqrt(2)) xx (1)/(sqrt(2)) +(1)/(sqrt(2)) xx (1)/(sqrt(2)) =(1)/(2)+(1)/(2)=1.`

Hence, `sin(A+B)=sinA cosB + cosA sinB.` [Proved]