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Question

If tanAtanB=x,cotBcotA=y, prove that cot(AB)=(1x)+(1y)

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Solution

cotBcotA=y

1(tanB)1(tanA)=y

tanAtanBtanAtanB=y
xy=tanAtanB

Now cot(AB)=1tan(AB)=1+tanAtanBtanAtanB=1+xyx=1x+1y

Hence Proved.

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