Question

SinA+cosB=a and sinB+cosA=b then sin(A+B)=

Answer 1

Step-by-step explanation:

sinA+cosB=a

(sinA+cosB)²=a².........(1)

sinB+cosA=b

(sinB+cosA)²=b².........(2)

(1)+(2)

(sinA+cosB)²+(sinB+cosA)²=a²+b²

sin²A+cos²B+2sinAcosB+sin²B+cos²A+ 2sinBcosA)=a²+b²

1+1+2(sinAcosB+cosAsinB)=a²+b²

2+2sin(A+B)=a²+b²

2sin(A+B)=a²+b²-2

sin(A+B)=a²+b²-2/2