Question

A solution of the equation tan^–1 (1 + x) + tan^–1 (1 – x) = $\frac { \pi } { 2 }$ is

• A. x = 1
• B. x = –1
• C. x = 0
• D. x = p

Answer 1

Answer: (C)

x = 0

Answer 2

tan^–1 (1 + x) + tan^–1 (1 –x) = $\frac { \pi } { 2 }$

̃ tan^–1 (1 + x) = $\frac { \pi } { 2 }$ – tan^–1 (1 –x)

̃ tan^–1 (1 + x) = cot^–1 (1 – x)

̃ tan^–1 (1 + x) = tan^–1 $\left( \frac { 1 } { 1 - x } \right)$

̃ 1 + x =̃ 1 – x² = 1

̃ x = 0