document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #785358 by KMST(5328) $\"\"$ $\"About$

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We are told that $\"A%2BB%2BC=180%5Eo\"$ , so $\"A%2BB=180%5Eo-C\"$
\n" ); document.write( "We (should) know that $\"tan%28180%5Eo-C%29=-tan%28C%29\"$ , so $\"tan%28A%2BB%29=-tan%28C%29\"$ .
\n" ); document.write( "According to the list of trigonometric identities that I found online
\n" ); document.write( " $\"tan%28A%2BB%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29\"$ , so
\n" ); document.write( " $\"-tan%28C%29=%28tan%28A%29%2Btan%28B%29%29%2F%281-tan%28A%29tan%28B%29%29\"$
\n" ); document.write( " $\"%28-tan%28C%29%29%281-tan%28A%29tan%28B%29%29=tan%28A%29%2Btan%28B%29\"$
\n" ); document.write( " $\"-tan%28C%29%2B%28-tan%28A%29tan%28B%29%29%28-tan%28C%29%29=tan%28A%29%2Btan%28B%29\"$
\n" ); document.write( " $\"-tan%28C%29%2Btan%28A%29tan%28B%29tan%28C%29=tan%28A%29%2Btan%28B%29\"$
\n" ); document.write( " $\"tan%28A%29tan%28B%29tan%28C%29=tan%28A%29%2Btan%28B%29%2Btan%28C%29\"$
\n" ); document.write( "and as we were told that $\"tan%28A%29%2Btan%28B%29%2Btan%28C%29=x\"$ , then
\n" ); document.write( " $\"highlight%28tan%28A%29tan%28B%29tan%28C%29=x%29\"$ \n" ); document.write( "

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