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General solution of $\tan θ + \tan 4 θ + \tan 7 θ = \tan θtan 4 θ \tan 7 θ$ is

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θ=nπ12, where n∈Z

θ=nπ9, where n∈Z

θ=nπ+π12, where n∈Z

none of these

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detailed solution

Correct option is D

From the given equation, we haveor tan⁡θ+tan⁡4θ1−tan⁡θtan⁡4θ=−tan⁡7θor tan⁡(θ+4θ)=−tan⁡7θor tan⁡5θ=tan⁡(−7θ)⇒5θ=nπ−7θor θ=nπ/12, where n∈Z, but n≠6,18,30,…

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General solution of tan⁡θ+tan⁡4θ+tan⁡7θ=tan⁡θtan⁡4θ tan7θ is

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General solution of $\tan θ + \tan 4 θ + \tan 7 θ = \tan θtan 4 θ \tan 7 θ$ is