Question

q = tan^–1 (2 tan²q) – tan^–1 $\left( \frac { 1 } { 3 } \tan \theta \right)$ then tan q =

• A. –2
• B. –1
• C. 2/3
• D. 2

Answer 1

Answer: (A)

–2

Answer 2

q = tan^–1 $\frac { 2 \tan ^ { 2 } \theta - \frac { 1 } { 3 } \tan \theta } { 1 + \frac { 2 } { 3 } \tan ^ { 3 } \theta }$

tan q = $\frac { 6 \tan ^ { 2 } \theta - \tan \theta } { 3 + 2 \tan ^ { 3 } \theta }$

1 = $\frac { 6 \tan \theta - 1 } { 3 + 2 \tan ^ { 3 } \theta }$ tan q = 0

2 tan³ q – 6 tan q + 4 = 0 ; (tan q –1)² (tan q + 2) = 0

tan q = 1; tan q = –2; tan q = 0