SOLUTION: tanA+cotB/tanB+cotA=tanA*cotB

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Question 1055474: tanA+cotB/tanB+cotA=tanA*cotB
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
%28tanA%2BcotB%29%2F%28tanB%2BcotA%29%22%22=%22%22tanA%2AcotB

We will use the fact that since tangent and cotangent are
reciprocals, that their product equals 1:

%22%22=%22%221

Indicate 1's multiplied by the terms on top:

%28tanA%2A1%2BcotB%2A1%29%2F%28tanB%2BcotA%29%22%22=%22%22

Substitute the products of a tangent by a cotangent
for the 1's: 

%28tanA%2A%28tanB%2AcotB%29%2BcotB%2A%28tanA%2AcotA%29%29%2F%28tanB%2BcotA%29%22%22=%22%22

Erase the unnecessary parentheses: 

%28tanA%2AtanB%2AcotB%2BcotB%2AtanA%2AcotA%29%2F%28tanB%2BcotA%29%22%22=%22%22

Factor tanA*cotB out if the numerator:

%28tanA%2AcotB%28tanB%2BcotA%29%29%2F%28tanB%2BcotA%29%22%22=%22%22

Cancel the tanB+cotA's

%28tanA%2AcotB%28cross%28tanB%2BcotA%29%29%29%2F%28cross%28tanB%2BcotA%29%29%22%22=%22%22

tanA%2AcotB

Edwin