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sin x+cos x=1/5 ==> find tan x

Source: 1978 AHSME Problem 15

June 6, 2014
trigonometryfunctionquadraticsAMC

Problem Statement

If sin⁡x+cos⁡x=1/5\sin x+\cos x=1/5 and 0≤x<π0\le x<\pi, then tan⁡x\tan x is
<spanclass=′latex−bold′>(A)</span>−43<spanclass=′latex−bold′>(B)</span>−34<spanclass=′latex−bold′>(C)</span>34<spanclass=′latex−bold′>(D)</span>43<span class='latex-bold'>(A) </span>-\frac{4}{3}\qquad<span class='latex-bold'>(B) </span>-\frac{3}{4}\qquad<span class='latex-bold'>(C) </span>\frac{3}{4}\qquad<span class='latex-bold'>(D) </span>\frac{4}{3}\qquad
<spanclass=′latex−bold′>(E)</span>not completely determined by the given information<span class='latex-bold'>(E) </span>\text{not completely determined by the given information}
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