If sin a= 12/13 and tan B 8/15 and angles a and b are in qundrant 1 find the value of tan (a+b)

Answer:The value of Tan (a + b) is [tex]\frac{-220}{21}[/tex] .Step-by-step explanation:Given as :Tan b = [tex]\frac{8}{15}[/tex]Sin a = [tex]\frac{12}{13}[/tex]∵Sin Ф = [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex]So,  [tex]\dfrac{\textrm perpendicular}{\textrm Hypotenuse}[/tex] =  [tex]\frac{12}{13}[/tex]Now, Base² = Hypotenuse² -  Perpendicular² Or, Base² = 13² - 12²Or,  Base² = 169 - 144Or,  Base² = 25∴     Base = [tex]\sqrt{25}[/tex] = 5And Tan Ф =  [tex]\dfrac{\textrm perpendicular}{\textrm Base}[/tex]Or, Tan a = [tex]\frac{12}{5}[/tex] Now, Tan (a + b) = [tex]\dfrac{Tan a + Tan b}{1- Tan a Tanb}[/tex]Or, Tan (a + b) = [tex]\frac{\frac{12}{5}+\frac{8}{5}}{1-(\frac{12}{5}\times \frac{8}{15})}[/tex]or, Tan (a + b) = [tex]\frac{\frac{36+8}{15}}{\frac{75-96}{75}}[/tex]or, Tan (a + b) =[tex]\frac{\frac{44}{15}}{\frac{-21}{75}}[/tex]Or, Tan (a + b) = [tex]\frac{-220}{21}[/tex]Hence The value of Tan (a + b) is [tex]\frac{-220}{21}[/tex] . Answer