Question

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

1. 3π/4 
2. π/4
3. π/3
4. π/6
5. None of these

Answer 1

Correct Answer - Option 2 : π/4

Concept:

\(\rm tan^{-1}x+tan^{-1}y =tan^{-1}\frac{x+y}{1-xy}\)

tan(π/4) = 1, tan(π -π/4) = tan(3π/4) = -1

 

Calculation:

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 

\(\rm tan^{-1}\frac{2+3}{1-(2)(3)}+C=π\\ =\rm tan^{-1}\frac{5}{-5}+C=π\)

⇒ tan^-1(-1) + C = π 

⇒ 3π/4 + C = π 

 ⇒C = π - 3π/4

= π/4 

Hence, option (2) is correct.