SOLUTION: Given three angles A, B, and C whose sum is 180 degrees. If tan A + tan B + tan C = x. Find the value of the product of the three tangents.

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Question 1161717: Given three angles A, B, and C whose sum is 180 degrees. If tan A + tan B + tan C = x. Find the value of the product of the three tangents.
Found 2 solutions by KMST, Edwin McCravy:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
We are told that , so
We (should) know that , so .
According to the list of trigonometric identities that I found online
, so





and as we were told that , then
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
We want to find:



we know 



Since (A+B+C=180^o}}} 





so substitute in



 





So  also.

[It's interesting that the product and the sum of the tangents
of the angles of a non-right triangle are the same.  A right
triangle contains a 90° and tan(90°) is not defined.]

Edwin
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