tanA+tanB/coA+cotB=tanAtanB
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(tan A+tan B) / (cot A+cot B)
⇒(tan A+tan B) / (1/tan A+1/tan B)
⇒(tan A +tan B) / (tan A+tan B / tan A·tan B)
⇒(tan A+tan B) / (tan A·tan B / tan A+tan B)
⇒tan A ·tan B
hence proved
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