Question

If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.

Options

• `(nπ ± sqrt(n^2π^2 + 32))/8`

• `(nπ ± sqrt(n^2 + 32))/8`

• `(nπ ± sqrt(π^2 + 32))/8`

• `(nπ ± sqrt(n^2 + 32))/16`

Answer 1

If tan 4θ = `tan(2/θ)`, then the general value of θ is `underlinebb((nπ ± sqrt(n^2π^2 + 32))/8)`.

Explanation:

tan 4θ = `tan(θ/2)`

∴ 4θ = `nπ + 2/θ`

∴ 4θ² – nπθ – 2 = 0

∴ θ = `(nπ ± sqrt(n^2π^2 + 32))/8`