Question

2sin²x +5cosx -4=0 ПОМОГИТЕ !!!!!!

Answer 1

$displaystyle 2sin^2x+5cosx-4=0\\2(1-cos^2x)+5cosx-4=0\\2-2cos^2x+5cosx-4=0\\-2cos^2x+5cosx-2=0\\2cos^2x-5cosx+2=0$

$displaystyle cosx=t\\2t^2-5t+2=0\\D=25-16=9\\t_{1.2}= frac{5pm 3}{4}\\t_1=2; t_2= frac{1}{2}\\cosx neq 2\\cosx= frac{1}{2}\\x=pm frac{ pi}{3}+2 pi n; nin Z$