Question

Cos2x + 10cosx - 11= 0

Answer 1

=cos^2x -sin^2 x +10cos x -11(cos^2 x +sin^ x)=cos^2 x -11cos^2x+10cos x -sin^2 x -11sin^2 x= 10cos x -10cos^2 x -12 sin^2 x=5cos^2 x +5cos^2 x+ 6sin x= 5cos^2 x +5cos^2 x+ 6(1-cos^2 x)=5cos^2 x +5cos^2 x+ 6 -6cos^2 x= cos^2 x -5cos x -6=0....замена cos  x= T... T^2 -5T-6=0
T=6
T=-1
Обрат. замена
cosx=6(не подходит)
cosx=-1. п+2пk