If `(cos e c^2theta-4)x^2+(cottheta+sqrt(3))x+cos^2(3pi)/2=0` holds true for all real `x ,` then the most general values of `theta` can be given by `n in Z)` `2npi+(11pi)/6` (b) `2npi+(5pi)/6` `2npi+-(7pi)/6` (d) `npi+-(11pi)/6`

Options

A. `2npi +(11 pi)/6`
B. `2n pi+(5 pi)/6`
C. `2n pi pm (7pi)/6`
D. `n pi pm (11 pi)/6`

Answer

A, B

Explanation

Given the quadratic equation is an identity. Therefore,
`cosec^(2) theta=4` and `cot theta=-sqrt(3)`
`rArr cosec theta=2` or `-2` and `tan theta=-1/sqrt(3)`
`theta=(5pi)/6` or `(11pi)/6`