Question

If tan β = cos θ tan α, then `tan^2  θ/2` = ______.

Options

• `(sin(α + β))/(sin(α - β))`

• `(cos(α - β))/(cos(α + β))`

• `(sin(α - β))/(sin(α + β))`

• `(cos(α + β))/(cos(α - β))`

Answer 1

If tan β = cos θ tan α, then `tan^2  θ/2` = `underlinebb((sin(α - β))/(sin(α + β)))`.

Explanation:

 `tan^2  θ/2 = (1 - cos θ)/(1 + cos θ)`

= `(tan α - tan β)/(tan α + tan β)`

= `sin(α - β)/sin(α + β)`