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Question

If tanA+tanB=a and cotA+ cotB=b, prove that: cot(A+B)= 1a1b.

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Solution

We have,
tanA+tanB=a and cotA+cotB=b
Now, cotA+cotB=b
1tanA+1tanB=b
tanB+tanAtanAtanB=b
ab=tanAtanB
cot(A+B)=1tan(A+B)
=1tanA+tanB1tanAtanB
=1aba
=baab
=babaab
=1a1b
cot(A+B)=1a1b
Hence proved.

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