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Equivalent Form of Trigonometric Function

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April 6, 2013
functiontrigonometryLaTeXsearchtrig identitiescosine double angle

Problem Statement

Let f(x)=sin⁡4x+4cos⁡2x−cos⁡4x+4sin⁡2xf(x)=\sqrt{\sin^4 x + 4\cos^2 x}-\sqrt{\cos^4x + 4\sin^2x}. An equivalent form of f(x)f(x) is
<spanclass=′latex−bold′>(A)</span>1−2sin⁡x<spanclass=′latex−bold′>(B)</span>−1+2cos⁡x<spanclass=′latex−bold′>(C)</span>cos⁡x2−sin⁡x2<span class='latex-bold'>(A) </span>1-\sqrt2\sin x\qquad<span class='latex-bold'>(B) </span>-1+\sqrt2\cos x\qquad<span class='latex-bold'>(C) </span>\cos\dfrac x2-\sin\dfrac x2 <spanclass=′latex−bold′>(D)</span>cos⁡x−sin⁡x<spanclass=′latex−bold′>(E)</span>cos⁡2x<span class='latex-bold'>(D) </span>\cos x-\sin x\qquad<span class='latex-bold'>(E) </span>\cos2x
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