Question

If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.

Options

• `63/52`

• `33/52`

• `63/16`

• `21/16`

Answer 1

If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to `underlinebb(63/16)`.

Explanation:

cos(α + β) = `3/5`	sin(α – β) = `5/13`

tan2α = tan[(α + β) + (α – β)]

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

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

= `63/16`