Question

5sin^2x+6cosx-6=0
помогите пожалуйста)

Answer 1

$5sin^2x+6cosx-6=0\\5(1-cos^2x)+6cosx-6=0\\5-5cos^2x+6cosx-6=0\\5cos^2x-6cosx+1=0\\5t^2-6t+1=0; ; ,; ; D/4=9-5=4; ,\\a); ; cosx= frac{3-2}{5} =frac{1}{5}\\underline {x=pm arccos frac{1}{5}+2pi n,; nin Z }\\b); ; cosx= frac{3+2}{5}=1 \\underline {x=2pi n,; nin Z}$