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If two angles of a triangle are tan^1,2 ...

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

A

`(pi)/(2)`

B

`(pi)/(3)`

C

`(pi)/(4)`

D

`(pi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given ,two angles of triangle are `tan^(-1)2andtan^(-1)3`. Let third angle be `theta` .Then ,
`tan^(-1)2+tan^(-1)3+theta=180^(@)`
`rArrtan^(-1)((2+3)/(1-2xx3))=180^(@)-theta`
`rArr(5)/(-5)=tan(180^(@)-theta)=-tantheta`
`rArrtantheta=1="tan"(pi)/(4)`
`rArrtheta=(pi)/(4)`
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