Question

The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.

Options

• `2"n"pi +- pi/6`

• `2"n"pi +- pi/4`

• `"n"pi + (-1)^"n" pi/3`

• `"n"pi + (-1)^"n" pi/4`

Answer 1

The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is `"n"pi + (-1)^"n" pi/3`.

Explanation:

`2sqrt(3) cos theta = tan theta`

⇒ `2sqrt(3) cos^2theta = sin theta`

⇒ `2sqrt(3) sin^2theta + sin theta - 2sqrt(3)` = 0

⇒ sin θ = `(-1 +- 7)/(4sqrt(3))`

⇒ sin θ = `(-8)/(4sqrt(3))`,

which is not possible

and sin θ = `6/(4sqrt(3)) = sqrt(3)/2 = sin  pi/3`

⇒ θ = `"n"pi + (-1)^"n" pi/3`