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Question

If tanαtanβ=m and cotαcotβ=n, then prove that cot(αβ)=1m1n

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Solution

tan(αβ)=tanαtanβ1+tanαtanβcot(αβ)=1+tanαtanβtanαtanβ....(1)cot(αβ)=1tanαtanβ+tanαtanβtanαtanβcotαcotβ=n1tanα1tanβ=n1+tanαtanβtanαtanβ=1n....(2)
From equation (1) and (2)
cot(αβ)=1m1n

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