Question

Найдите значение выражения:
ctg²П/3×cos²П/3+cos²П/3-ctg²П/3 ​

Answer 1

Ответ:

$ctg^2\dfrac{\pi}{3}\cdot cos^2\dfrac{\pi}{3}+cos^2\dfrac{\pi}{3}-ctg^2\dfrac{\pi}{3}=\Big(\dfrac{\sqrt3}{3}\Big)^2\cdot \Big(\dfrac{1}{2}\Big)^2+\Big(\dfrac{1}{2}\Big)^2-\Big(\dfrac{\sqrt3}{3}\Big)^2=\\\\\\=\dfrac{1}{3}\cdot \dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{3}=\dfrac{1}{12}+\dfrac{1}{4}-\dfrac{1}{3}=\dfrac{1+3-4}{12}=\dfrac{0}{12}=0$