Question

If `A=B=45^(@)`, then justify
`sin(A+B)=sinA cosB+cosA sinB.`

Answer 1

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]