Find, `theta =tan^(-1) (2 tan^(2) theta) - tan^(-1) ((1)/(3) tan theta) " then " tan theta=`

Options

A. `-2`
B. `-1`
C. `2//3`
D. 2

Answer

A

Explanation

`theta = tan^(-1) (2 tan^(2) theta) - tan^(-1) ((1)/(3) tan theta) = tan^(-1).(2 tan^(2) theta - (1)/(3) tan theta)/(1 + (1)/(3) tan^(3) theta)`
`rArr tan theta = (6 tan^(2) theta - tan theta)/(3 + 2 tan^(3) theta)`
`rArr 1 = (6 tan theta -1)/(3 + 2 tan^(3) theta) " or " tan theta = 0`
`rArr 2 tan^(3) theta - 6 tan theta + 4 = 0 " or " tan theta = 0`
`rArr (tan theta 1)^(2) (tan theta + 2) = 0 " or " tan theta = 0`
`rArr tan theta =1, tan theta = -2, tan theta = 0`