Question

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 1

Answer:

The value of Tan (a + b) is $\frac{-220}{21}$ .

Step-by-step explanation:

Given as :

Tan b = $\frac{8}{15}$

Sin a = $\frac{12}{13}$

∵Sin Ф = $\dfrac{\textrm perpendicular}{\textrm Hypotenuse}$

So,  $\dfrac{\textrm perpendicular}{\textrm Hypotenuse}$ =  $\frac{12}{13}$

Now, Base² = Hypotenuse² -  Perpendicular²

Or, Base² = 13² - 12²

Or,  Base² = 169 - 144

Or,  Base² = 25

∴     Base = $\sqrt{25}$ = 5

And Tan Ф =  $\dfrac{\textrm perpendicular}{\textrm Base}$

Or, Tan a = $\frac{12}{5}$

Now, Tan (a + b) = $\dfrac{Tan a + Tan b}{1- Tan a Tanb}$

Or, Tan (a + b) = $\frac{\frac{12}{5}+\frac{8}{5}}{1-(\frac{12}{5}\times \frac{8}{15})}$

or, Tan (a + b) = $\frac{\frac{36+8}{15}}{\frac{75-96}{75}}$

or, Tan (a + b) =$\frac{\frac{44}{15}}{\frac{-21}{75}}$

Or, Tan (a + b) = $\frac{-220}{21}$

Hence The value of Tan (a + b) is $\frac{-220}{21}$ . Answer