Question

Определи знак разности ctg7π/13−ctg4π/13 (знак) 0

Answer 1

Ответ:

$ctg(\frac{7\pi}{13} )-ctg(\frac{4\pi}{13} )<0$

Объяснение:

$ctg(\frac{7\pi}{13} )-ctg(\frac{4\pi}{13} ) = ctg(\frac{-4\pi}{13}+\pi )-ctg(\frac{4\pi}{13} )=ctg(\frac{-4\pi}{13})-ctg(\frac{4\pi}{13} ) =\\\\=-ctg(\frac{4\pi}{13})-ctg(\frac{4\pi}{13} ) = -2ctg(\frac{4\pi}{13} ) \\\\\frac{4\pi}{13} \in I\ =>\ ctg\frac{4\pi}{13} > 0 => -2ctg(\frac{4\pi}{13} )<0 =>ctg(\frac{7\pi}{13} )-ctg(\frac{4\pi}{13} )<0$