MathDB
Function in Sine and Cosine

Source:

April 6, 2013
functiontrigonometry

Problem Statement

Let fn(x)=sin⁡nx+cos⁡nxf_n(x)=\sin^n x + \cos^n x. For how many xx in [0,π][0,\pi] is it true that 6f4(x)−4f6(x)=2f2(x)?6f_4(x)-4f_6(x)=2f_2(x)? <spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>4<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>more than 8<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>4\qquad<span class='latex-bold'>(C) </span>6\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>\text{more than 8}
Back to ProblemsView on AoPS