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Question

If cotαcotβ=2 then cos(α+β)cos(αβ) is equal to

A
3
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B
23
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C
13
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D
tanαtanβ
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Solution

The correct option is B 13
Given, cotαcotβ=2, then
cos(α+β)cos(αβ)=cosαcosβsinαsinβcosαcosβ+sinαsinβ=cotαcotβ1cotαcotβ+1=212+1=13

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