Question

The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is ______.

Options

• θ = `(nπ)/4`

• θ = `(nπ)/12`

• θ = `(nπ)/6`

• None of these

Answer 1

The general solution of the equation tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ is `underlinebb(θ = (nπ)/12)`.

Explanation:

We write the given equation as

tan θ + tan 4θ = – tan 7θ(1 – tan θ tan 4θ)

`\implies` tan(θ + 4θ) = – tan 7θ

`\implies` tan 5θ = tan(– 7θ)

∴ 5θ = nπ + (– 7θ) or 12θ = nπ

∴ θ = `(nπ)/12`, n ∈ I