Тангенс и котангенс угла. Задача 12math100admin44242025-03-21T18:23:28+03:00
Задача 12. Вычислите \(\dfrac{{\sqrt {12} }}{5}\left( {{\text{tg}}\dfrac{{59\pi }}{6}-{\text{ctg}}\dfrac{{40\pi }}{3}} \right)\)
Решение
\(\dfrac{{\sqrt {12} }}{5}\left( {{\rm{tg}}\dfrac{{59\pi }}{6}-{\rm{ctg}}\dfrac{{40\pi }}{3}} \right) = \dfrac{{\sqrt {12} }}{5}\left( {{\rm{tg}}\left( {\dfrac{{59\pi }}{6}-10\pi } \right)-{\rm{ctg}}\left( {\dfrac{{40\pi }}{3}-13\pi } \right)} \right) = \)
\( = \dfrac{{\sqrt {12} }}{5}\left( {{\rm{tg}}\left( {-\dfrac{\pi }{6}} \right)-{\rm{ctg}}\dfrac{\pi }{3}} \right) = \dfrac{{\sqrt {12} }}{5}\left( {-\dfrac{1}{{\sqrt 3 }}-\dfrac{1}{{\sqrt 3 }}} \right) = -\dfrac{{2\sqrt {12} }}{{5\sqrt 3 }} = -\dfrac{{2\sqrt 4 }}{5} = -\dfrac{4}{5} = -0,8.\)
Ответ: \(-0,8.\)