Question

Решать Уравнение 6sin^2 x- 5sinx+1=0

Answer 1

$6sin^2x-5sinx+1=0\ sinx=t, t in [-1;1]\ 6t^2-5t+1=0\ D=(-5)^2-4cdot6cdot1=25-24=1\ t_1= frac{5+1}{12}= frac{6}{12} = frac{1}{2} \ t_2= frac{5-1}{12}= frac{4}{12} = frac{1}{3} \ ====================\ sinx= frac{1}{2} \ x=(-1)^k arcsin frac{1}{2}+ pi k, k in Z\ x=(-1)^k frac{ pi }{6}+ pi k, k in Z\ ====================\ sinx= frac{1}{3} \ x=(-1)^n arcsin frac{1}{3}+ pi n, n in Z$