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