Question

If `sin(theta + pi/6) = 4cos(theta - pi/3)`, then tan θ = ______

Options

• `sqrt3`

• `-1/sqrt3`

• `1/sqrt3`

• `-sqrt3`

Answer 1

If `sin(theta + pi/6) = 4cos(theta - pi/3)`, then tan θ = `underline(-1/sqrt3)`.

Explanation:

`sin(theta + pi/6) = 4cos(theta - pi/3)`

∴ `sin theta . cos  pi/6 + costheta . sin  pi/6 = 4(costheta . cos  pi/3 + sin theta . sin  pi/3)`

⇒ `sqrt3/2 sintheta + 1/2 costheta = 4(1/2costheta + sqrt3/2 sintheta)`

⇒ `costheta + sqrt3 sintheta = 0`

⇒ tan θ = `-1/sqrt3`