Question

$cos2x+3sinx geq -1$

Answer 1

$cos2x+3sinx geq -1 \ 1-2sin^{2} x+3sinx geq -1 \ 2sin^{2} x-3sinx-2 leq 0 \ a=sinx, |a| leq 1 \ 2a^{2} -3a-2 leq 0 \ D = 9 + 4*4 = 25 = 5^2 \ a= frac{3+5}{4}=2 textgreater 1 \ a= frac{3-5}{4} = - frac{1}{2} \ - frac{1}{2} leq sinx leq 1 \ - frac{ pi }{6} +2 pi k leq x leq frac{7 pi }{6} +2 pi n; k,n - Z$