The given equation is
[tex]8cos(x)+ 4 sin(2x)=0[/tex]
Using the double angle formula of sin(2x),
[tex]8cos(x) +4(2) sin(x)cos(x)=0[/tex]
[tex]8cos(x)+ 8 sin(x) cos(x)=0[/tex]
Taking out 8 cos x
[tex]8cos(x) (1+ sin(x)) =0[/tex]
[tex]8 cos(x)=0 , 1+sin (x)=0
\\
8cos (x)=0, sin(x)=-1
\\
cos(x)=0 , sin(x)=-1
\\
x = \frac{ \pi}{2} , \frac{ 3 \pi}{2}[/tex]
And that's the required answer.
