Write the solution set of the equation `(2costheta+1)(4costheta+5)=0` in the interval `[0,2pi]`

Options

A. `theta = (2pi)/3,(4pi)/3.`

B. `theta = (pi)/3,(4pi)/3.`

C. `theta = (2pi)/3,(pi)/3.`

D. `theta = (pi)/3,(5pi)/3.`

Answer

A

Explanation

`(2costheta+1)(4costheta+5) = 0`

`=>(2costheta+1) = 0 or (4costheta+5) = 0`

`=>costheta = -1/2 or cos theta = -5/4`

But, minimum value of `cos theta` is `-1`, so `costheta != -5/4.`

`:. costheta = -1/2`

`=>theta = (2pi)/3,(4pi)/3.`