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

The value of Tan (a + b) is
`(-220)/(21)` .

Explanation:

Given as :

Tan b =
`(8)/(15)`

Sin a =
`(12)/(13)`

∵Sin Ф =
`(\textrm perpendicular)/(\textrm Hypotenuse)`

So,
`(\textrm perpendicular)/(\textrm Hypotenuse)` =
`(12)/(13)`

Now, Base² = Hypotenuse² - Perpendicular²

Or, Base² = 13² - 12²

Or, Base² = 169 - 144

Or, Base² = 25

∴ Base =
`√(25)` = 5

And Tan Ф =
`(\textrm perpendicular)/(\textrm Base)`

Or, Tan a =
`(12)/(5)`

Now, Tan (a + b) =
`(Tan a + Tan b)/(1- Tan a Tanb)`

Or, Tan (a + b) =
`((12)/(5)+(8)/(5))/(1-((12)/(5)* (8)/(15)))`

or, Tan (a + b) =
`((36+8)/(15))/((75-96)/(75))`

or, Tan (a + b) =
`((44)/(15))/((-21)/(75))`

Or, Tan (a + b) =
`(-220)/(21)`

Hence The value of Tan (a + b) is
`(-220)/(21)` . Answer