If `tan^(- 1)\ 1/4+tan^(- 1)\ 2/9=1/2cos^(- 1)x` then `x` is equal to

Options

A. `(1)/(2)tan^(-1)((4)/(3))`
B. `2tan^(-1)(5)`
C. `(1)/(2)tan^(-1)((6)/(5))`
D. None of these

Answer

D

Explanation

`tan^(-1)((1)/(4))+2tan^(-1)((2)/(9))`
`=2[tan^(-1)((1)/(4))+tan^(-1)((2)/(8))]`
`=2tan^(-1)(((1)/(4)+(2)/(9))/(1-(1)/(4)xx(2)/(9)))=2tan^(-1)((17)/(34))`
`=2tan^(-1)((1)/(2))`
`=tan^(-1)((2(1)/(2))/(1-((1)/(2))^(2)))=tan^(-1)((4)/(3))`