5

Part of 1968 German National Olympiad

Problems(1)

sin x +1/2 sin 2x +1/3 sin 3x > 0

Source: 1967-68 Germany R4 12.5

Prove that for all real numbers

x

of the interval

0 < x <\pi

\sin x +\frac12 \sin 2x +\frac13 \sin 3x > 0

algebrainequalitiestrigonometry