Тангенс и котангенс угла. Задача 4math100admin44242025-03-21T18:10:28+03:00
Задача 4. Вычислите \(\dfrac{1}{{\sqrt 3 }}\,\,{\text{ctg}}\dfrac{{7\pi }}{6}-\sqrt {12} \,{\text{tg}}\dfrac{{4\pi }}{3}\)
Решение
\(\dfrac{1}{{\sqrt 3 }}{\rm{ctg}}\dfrac{{7\pi }}{6}-\sqrt {12} {\rm{tg}}\dfrac{{4\pi }}{3} = \dfrac{1}{{\sqrt 3 }}{\rm{ctg}}\left( {\dfrac{{7\pi }}{6}-\pi } \right)-\sqrt {12} {\rm{tg}}\left( {\dfrac{{4\pi }}{3}-\pi } \right) = \)
\( = \dfrac{1}{{\sqrt 3 }}{\rm{ctg}}\dfrac{\pi }{6}-\sqrt {12} {\rm{tg}}\dfrac{\pi }{3} = \dfrac{1}{{\sqrt 3 }} \cdot \sqrt 3 -\sqrt {12} \cdot \sqrt 3 = 1-6 = -5.\)
Ответ: \(-5.\)