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)

Question

asked Feb 13, 2020 149k views

1 Answer

Amer Bearat · Answer 1 · 2020-02-18T04:28:43+0000

Answer:

The value of Tan (a + b) is
.

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 =
= 5

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

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

Now, Tan (a + b) =

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
. Answer