Difference between revisions of "2007 iTest Problems/Problem 17"

Revision as of 05:12, 30 July 2016

If $x$ and $y$ are acute angles such that $x+y=\frac{\pi}{4}$ and $\tan{y}=\frac{1}{6}$ , find the value of $\tan{x}$ .

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 If <math>x</math> and <math>y</math> are acute angles such that <math>x+y=\frac{\pi}{4}</math> and <math>\tan{y}=\frac{1}{6}</math>, find the value of <math>\tan{x}</math>.
-<math> \text{(A) }\frac{37\sqrt{2}-18}{71}\qquad
-\text{(B) }\frac{35\sqrt{2}-6}{71}\qquad
-\text{(C) }\frac{35\sqrt{3}+12}{33}\qquad
-\text{(D) }\frac{37\sqrt{3}+24}{33}\qquad
-\text{(E) }1\qquad
-\text{(F) }\frac{5}{7}\qquad \\ </math>
-<math>\text{(G) }\frac{3}{7}\qquad
-\text{(H) }6\qquad
-\text{(I) }\frac{1}{6}\qquad
-\text{(J) }\frac{1}{2}\qquad
-\text{(K) }\frac{6}{7}\qquad
-\text{(L) }\frac{4}{7}\qquad \\ </math>
-<math>\text{(M) }\sqrt{3}\qquad
-\text{(N) }\frac{\sqrt{3}}{3}\qquad
-\text{(O) }\frac{5}{6}\qquad
-\text{(P) }\frac{2}{3}\qquad
-\text{(Q) }\frac{1}{2007}\qquad\\ </math>
 == Solution ==