Question

if sin A + cos B = a and sin B + cos A = b, then sin (A+B) is equal to

Answer 1

sinA cosB+cosA sinB

Answer 2

sinA +coaB=a
cosB=a-sinA

sinB+cosA=b
sinB=b-cosA

now, sin(a+b)=sinAcosB+cosAsinB
=sinA(a-sinA) + cosA(b-cosA)
=asinA-sin^2A+bcosA-cos^2A
=asinA+bcosA-1