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If $\tan θ + \tan ϕ = a, \cot θ + \cot ϕ = b, θ - ϕ = α (\neq 0)$ then

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ab<4

ab=4

ab>4

ab=0

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detailed solution

Correct option is C

ab=tan⁡θtan⁡ϕ,tan2⁡α=tan2⁡(θ−φ)=tan⁡θ−tan⁡ϕ1+tan⁡θtan⁡ϕ2 =a2−4(a/b)1+(a/b)2=ab(ab−4)(a+b)2Since tan2⁡a>0,ab>4

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If tan⁡θ+tan⁡ϕ=a,cot⁡θ+cot⁡ϕ=b,θ−ϕ=α(≠0) then

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If $\tan θ + \tan ϕ = a, \cot θ + \cot ϕ = b, θ - ϕ = α (\neq 0)$ then