Question

If the sum of the acute angles tan^–1 x and tan^–1 $\left( \frac { 1 } { 2 } \right)$ is 45⁰, then value of x is

• A. $\frac { 1 } { 2 }$
• B. $\frac { 1 } { 3 }$
• C. $\frac { 1 } { 4 }$
• D. $\frac { 1 } { 5 }$

Answer 1

Answer: (B)

$\frac { 1 } { 3 }$

Answer 2

We have, tan^–1 x + tan^–1 $\left( \frac { 1 } { 2 } \right)$= 45⁰

Ž tan^–1x = 45⁰ – tan^–1 $\left( \frac { 1 } { 2 } \right)$

Ž tan^–1x = tan^–1 (1) – tan^–1 $\left( \frac { 1 } { 2 } \right)$

Ž tan^–1 x = tan^–1 = tan^–1 $\left( \frac { 1 } { 3 } \right)$ Ž x = $\frac { 1 } { 3 }$