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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)

1 Answer

4 votes

Answer:

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

User Amer Bearat
by
8.1k points

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