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If $2 \tan α + \cot β = \tan β$ , then the value of $\tan (β - α)$ is

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detailed solution

Correct option is D

tan⁡(β−α)=tan⁡β−tan⁡α1+tan⁡βtan⁡α=tan⁡α+cot⁡β1+tan⁡βtan⁡α=tan⁡αtan⁡β+1tan⁡β(1+tan⁡αtan⁡β)=cot⁡β

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If 2tan⁡α+cot⁡β=tan⁡β , then the value of tan⁡(β−α) is

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If $2 \tan α + \cot β = \tan β$ , then the value of $\tan (β - α)$ is