Question

решите пожалуйста;4cos²x-11sinx-1=0​

Answer 1

4Cos²x - 11Sinx - 1 = 0

4 * (1 - Sin²x) - 11Sinx - 1 = 0

4 - 4Sin²x - 11Sinx - 1 = 0

- 4Sin²x - 11Sinx + 3 = 0

4Sin²x + 11Sinx - 3 = 0

D = 11² - 4 * 4 * (- 3) = 121 + 48 = 169 = 13²

$1)Sinx = \frac{-11+13}{8}=\frac{1}{4}\\\\x=(-1)^{n}arc Sin\frac{1}{4}+\pi n,n\in Z\\\\2)Sinx=\frac{-11-13}{8}=- 3<-1-neyd\\\\Otvet:\boxed{(-1)^{n}arc Sin\frac{1}{4}+\pi n,n\in Z}$