Question

Решите уравнение 6sin^2x-5sinx=-1

Answer 1

6sin^2x -5sinx+1=0
sinx=t

6t²-5t+1=0
D=25-24=1
t1=5+1/12=6/12=1/2
t2=5-1/12=4/12=1/3

sinx=1/2
x=π/6+πn

sinx=1/3
x=arcsin 1/3 + πn

Answer 2

$6\sin^2x-5\sin x=-1\\6\sin^2x-5\sin x+1=0\\\sin x=t,\;\sin^2x=t^2,\;t\in[-1;\;1]\\6t^2-5t+1=0\\D=25-4\cdot6\cdot1=1\\t_{1,2}=\frac{5\pm1}{12}\\t_1=\frac13\\t_2=\frac12\\\sin x=\frac13\Rightarrow x=(-1)^n\cdot\arcsin\left(\frac13\right)+\pi n\\\sin x=\frac12\Rightarrow x(-1)^n\cdot\frac\pi6+\pi n,\;n\in\mathbb{Z}$