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Question

If tanA−tanB=xandcotB−cota=y , then the value of cot(A−B) is

A
x-y
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B
x+y
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C
1x1y
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D
1x+1y
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Solution

The correct option is D 1x+1y
cotBcotA=y
tanAtanB
or tanAtanBtanAtanB=y
or tanAtanB=xy
Now, cot(AB)=1tan(AB)=1+tanAtanBtanAtanB
=1+xyx=1x+1y

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