MathDB
A trignometric eqn

Source: Indian IMOTC 2005 Day 5 Problem 3

September 23, 2005
functiontrigonometryinequalitiesalgebra unsolvedalgebra

Problem Statement

For real numbers a,b,c,da,b,c,d not all equal to 00 , define a real function f(x)=a+bcos⁡2x+csin⁡5x+dcos⁡8xf(x) = a +b\cos{2x} + c\sin{5x} +d \cos{8x}. Suppose f(t)=4af(t) = 4a for some real tt. prove that there exist a real number ss s.t. f(s)<0f(s)<0
Back to ProblemsView on AoPS