Question

-sin2 x -8 cos x+8=0

Answer 1

$-sin^2x-8cosx+8=0 \ -(1-cos^2x)-8cosx+8=0 \ -1+cos^2x-8cosx+8=0 \ cos^2x-8cosx+7=0 \ D_1=16-7=9 \ cosx_1 neq 4+3>1 \ cosx_2 =4-3=1 \ x=2pi n, nin Z$
Ответ: 2пn, где n - целые числа

Answer 2

-sin^x+8(1-cosx)=0
-4sin^x/2cos^x/2+16sin^2x/2=0
4sin^x/2(4-cos^2x/2)=0
sin^x/2=0
x=2Пk
4-cos^x/2=0  |cosx|<=1