If two angles of a triangle are `tan^1,2` and `tan^1,3`, what is the third angle.

Options

A. `tan^(-1)2`
B. `tan^(-1)4`
C. `pi//4`
D. `pi//3`

Answer

C

Explanation

Let `A = tan^(-1)2, B = tan^(-1)3 and C` be the angles of a triangle.
By angle sum property, we have
`tan^(-1)2 + tan^(-1)3 + C = 180^(@)`
`rArr tan^(-1)((5)/(-5))=180^(@)-C`
`rArr tan^(-1)(-1)=180^(@) - C`
`rArr (3pi)/(4)=pi-C rArr C = pi -(3pi)/(4)=(pi)/(4)`
Hence, third angle is `(pi)/(4)`.