Question

If tan^-1 2, tan^-1 3 are two angles of a triangle then what is the third angle

Answer 1

Answer:

Step-by-step explanation:

1st angle--- tanФ1=2

2nd angle---- tanФ2=3

3rd angle---- tanФ3= ???

we know in a triangle Ф1+Ф2+Ф3= 180°

so Ф1+Ф2= 90°- Ф3-------(a)

tanФ1.tanФ2= 6-------(1)

tanФ1+ tanФ2= 5-----(2)

we can use property of $tan(\alpha +\beta ) = \frac{tan\alpha + tan\beta  }{1-tan\alpha.tan\beta  }$

and 90°-Ф3= Ф1+Ф2 from (a)

using 1 and 2

putting we get tan(90°- Ф3) = 5/(1-6)

cot(Ф3)= -1

Ф3= 135°, 315°, 495°,675° and so on

hope it helps :))