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Q.

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

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a

ab<4

b

ab=4

c

ab>4

d

ab=0

answer is C.

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Detailed Solution

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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