напишите пример 9+6tg(x/6+2)=3. Created by pavelsmolskiy. algebra-ru

6+2)=3...

Хуqожнuк $9+6tg( \frac{x}{6} +2) = 3\\\\6tg( \frac{x}{6}+2)=-6\\\\tg( \frac{x}{6}+2)= - 1\\\\ \frac{x}{6}+2=- \frac{ \pi }{4} + \pi n \\\\ \frac{x}{6}=- \frac{ \pi }{4}-2+ \pi n\\\\x=- \frac{3 \pi }{2}-12 +6 \pi n$

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9 + 6tg(x/6 + 2) = 3
6tg(x/6 + 2) = -6
tg(x/6 + 2) = -1
x/6 + 2 = -π/4 + πk
x/6 = -π/4 - 2 + πk
x = -3π/2 - 12 + 6πk

k∈Z

ОДЗ: tg(x/6 + 2) - существует
cos(x/6 + 2) ≠ 0
x/6 + 2 ≠ π/2 + πk
x/6 ≠ π/2 - 2 + πk
x ≠ 3π - 12 + 6πk

Ответ: -3π/2 - 12 + 6πk, k∈Z

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