Question

If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.

Options

• `25/16`

• `56/33`

• `19/12`

• `20/7`

Answer 1

If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to `underlinebb(56/33)`.

Explanation:

Given, cos (α + β) = `4/5`

`\implies` α + β ∈ Ist quadrant and sin (α – β) = `5/13`

`\implies` α – β ∈ Ist quadrant

∵ 2α = (α + β) + (α – β)

∴ tan 2α = `(tan(α + β) + tan (α - β))/(1 - tan (α + β) tan (α - β))`

= `(3/4 + 5/12)/(1 - 3/4 . 5/12)`

= `56/33`