UPSC NDA Math Model Paper 4

Given: tan−1(2),tan−1(3) are two angles of a triangle
Let, C be the third angles of a triangle.
As we know, sum of angle in triangle is equal to 180°
So, tan−1(2)+tan−1(3)+C=π
tan−1

2+3

1−(2)(3)

+C=π
=tan−1

5

−5

+C=π
⇒tan−1(−1)+C=π
⇒3π∕4+C=π
⇒C=π−3π∕4
=π∕4
Hence, option ( 2 ) is correct.