Question

помогите решить тригоном. ур-е : 3+9cosx=5sin^2 x

Answer 1

$5 sin^{2} x-9cosx-3=0 \ 5(1- cos^{2} x)-9cosx-3=0 \ 5-5 cos^{2} x-9cosx-3=0 \ 5cos^{2}x+9cosx-2=0 \ D= sqrt{81 +4*2*5} =11 \ cosx= frac{-9+11}{10} = frac{1}{5} \ cosx= frac{-9-11}{10} =-2$$-1leq cos alpha leq 1$$cosx= frac{1}{5} \ x=arccos frac{1}{5} +2 pi n \ x=-arccos frac{1}{5} +2 pi n$