Question

If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.

Options

• `(1 + k)/(1 - k)`

• `(1 - k)/(1 + k)`

• `(k + 1)/(k - 1)`

• `(k - 1)/(k + 1)`

Answer 1

If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to `underlinebb((1 + k)/(1 - k))`.

Explanation:

∵ tan α = k cot β or tan α tan β = k

Now, `(cos(α - β))/(cos(α + β))`

= `(cos α cos β + sin α sin β)/(cos α cos β - sin α sin β)`

= `(1 + tan α tan β)/(1 - tan α tan β)`

= `(1 + k)/(1 - k)`