Answer:
[tex]sin(A+B) = \frac{1431}{1769}[/tex]
Step-by-step explanation:
sin(A+B) = sinA cosB + cosA sinB ------(1)
[tex]given : cos A = \frac{20}{29}, \ sinB = \frac{60}{61}[/tex]
First we will find sinA and cosB
[tex]We \ know \ sin^2 A + cos^2A = 1\\\\sin^2 A = 1 - cos^2A = 1 - (\frac{20}{29})^{2} = \frac{841-440}{841} = \frac{441}{841}\\\\sinA =\frac{21}{29}[/tex]
[tex]sin^2B +cos^2B = 1\\\\cos^2B = 1 - sin^2B = 1 - (\frac{60}{61})^2 = \frac{3721-3600}{3721} = \frac{121}{3721}\\\\cosB = \frac{11}{61}[/tex]
Substitute all values in (1)
[tex]sin(A+B) =sinAcosB + cosAsinB[/tex]
[tex]=(\frac{21}{29} \times \frac{11}{61} )+ (\frac{20}{29}\times \frac{60}{61})\\\\=\frac{231}{1769} + \frac{1200}{1769}\\\\= \frac{1431}{1769}[/tex]
