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 - 12²
Or, Base² = 169 - 144
Or, Base² = 25
∴ Base = [tex]\sqrt{25}[/tex] = 5
And 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
