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Trig identities

Source: AHSME 1991 problem 21

October 30, 2011
trigonometryAMC

Problem Statement

If f(xx−1)=1xf\left(\frac{x}{x - 1}\right) = \frac{1}{x} for all x≠0,1x \ne 0,1 and 0<θ<π20 < \theta < \frac{\pi}{2}, then f(sec⁡2θ)=f(\sec^{2}\theta) =
<spanclass=′latex−bold′>(A)</span>sin⁡2θ<spanclass=′latex−bold′>(B)</span>cos⁡2θ<spanclass=′latex−bold′>(C)</span>tan⁡2θ<spanclass=′latex−bold′>(D)</span>cot⁡2θ<spanclass=′latex−bold′>(E)</span>csc⁡2θ <span class='latex-bold'>(A) </span>\sin^{2}\theta\qquad<span class='latex-bold'>(B) </span>\cos^{2}\theta\qquad<span class='latex-bold'>(C) </span>\tan^{2}\theta\qquad<span class='latex-bold'>(D) </span>\cot^{2}\theta\qquad<span class='latex-bold'>(E) </span>\csc^{2}\theta
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