[tex]|tg(x) + ctg(x)| \geq 2[/tex]
tg(x) + ctg(x)
[tex] \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} [/tex]
[tex] \frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)} [/tex]
[tex] \frac{1}{ \frac{1}{2}sin(2x) } [/tex]
[tex] \frac{2}{sin(2x)} [/tex]
2 csc(2x)
[tex]|csc(2x)| \geq 1 [/tex] pentru orice x, atunci
[tex]|2csc(2x)| \geq 2[/tex] => [tex]|tg(x)+ctg(x)| \geq 2[/tex]
