Тангенс и котангенс угла. Задача 11math100admin44242025-03-21T18:21:47+03:00
Задача 11. Вычислите \(\dfrac{1}{{\sqrt 3 }}{\text{tg}}\dfrac{{29\pi }}{3}-\dfrac{{\sqrt 3 }}{2}{\text{ctg}}\dfrac{{34\pi }}{3}\)
Решение
\(\dfrac{1}{{\sqrt 3 }}{\rm{tg}}\dfrac{{29\pi }}{3}-\dfrac{{\sqrt 3 }}{2}{\rm{ctg}}\dfrac{{34\pi }}{3} = \dfrac{1}{{\sqrt 3 }}{\rm{tg}}\left( {\dfrac{{29\pi }}{3}-10\pi } \right)-\dfrac{{\sqrt 3 }}{2}{\rm{ctg}}\left( {\dfrac{{34\pi }}{3}-11\pi } \right) = \)
\( = \dfrac{1}{{\sqrt 3 }}{\rm{tg}}\left( {-\dfrac{\pi }{3}} \right)-\dfrac{{\sqrt 3 }}{2}{\rm{ctg}}\dfrac{\pi }{3} = \dfrac{1}{{\sqrt 3 }} \cdot \left( {-\sqrt 3 } \right)-\dfrac{{\sqrt 3 }}{2} \cdot \dfrac{1}{{\sqrt 3 }} = -1-0,5 = -1,5.\)
Ответ: \(-1,5.\)