Nierownosci

[kur4s]

\(\displaystyle{ cosx sin3x > sinx cos3x}\)
\(\displaystyle{ cosx + tgx < 1 + sinx}\)
\(\displaystyle{ 4sinx + \frac{2sinx}{sin2x} < 2tgx + 2}\)
\(\displaystyle{ \frac{cos2x + cosx - 1}{cos2x} >2}\)
\(\displaystyle{ \frac{1 + 2cosx}{sinx} < 0}\)
\(\displaystyle{ cos2x + \frac{cosx}{ \sqrt{3} } - 1 < 0}\)

[Wicio]

5)
\(\displaystyle{ \frac{1 + 2cosx}{sinx} < 0}\)
\(\displaystyle{ (1 + 2cosx)(sinx) < 0}\)

\(\displaystyle{ 1+2cos x=0}\)
\(\displaystyle{ cos x=- \frac{1}{2}}\)
\(\displaystyle{ x=- \frac{\pi}{3}+2k \pi}\)

\(\displaystyle{ sin x=0}\)
\(\displaystyle{ x=k \pi}\)

Więc \(\displaystyle{ (1 + 2cosx)(sinx) < 0}\) gdy \(\displaystyle{ x ( - \frac{\pi}{3}+2k \pi, 2k \pi)}\)