Question

решите уравнение 2 sin²x+cos x–1=0

Answer 1

2(1-cos^2x) + cos x - 1 =0;
 2 - 2 cos^2 x  +cos x -1 =0;
- 2 cos^2 x + cos x +1 =0;
 2 cos^2 x - cos x - 1 =0;
cos x =t;  -1 ≤ t≤ 1;
2t^2 -t - 1=0;
 D=1+8=93^2;
 t1= 1;⇒ cos x =1; ⇒x = 2pik; k∈Z;
t2= -1/2; ⇒cos x = -1/2; ⇒ x = + - pi/3 + 2pin; n∈Z