Question

If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.

Options

• `sqrt(3)`

• `-1/sqrt(3)`

• `1/sqrt(3)`

• `-sqrt(3)`

Answer 1

If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = `underlinebb(-sqrt(3))`.

Explanation:

`2sin(θ + π/3) = cos(θ - π/6)`

`\implies 2[sinθ cos  π/3 + cos θ sin  π/3] = cos θ cos  π/6 + sin θ sin  π/6`

`\implies 2[sinθ/2 + cosθ (sqrt(3)/2)] = cosθ(sqrt(3)/2) + sinθ(1/2)`

`\implies sin θ + sqrt(3)cosθ = sqrt(3)/2 cosθ + 1/2 sinθ`

`\implies 1/2 sinθ = (-sqrt(3))/2 cos θ`

`\implies` tan θ = `-sqrt(3)`