i wonder if this is right :)

4 sin^2(x) + 8 cos(x) = 7

1 = cosē(x)+sinēx

sinē(x) = 1-cosē(x)

replace sinē(x) with 1-cosē(x)

-4cosē(x)+8cos(x)+4 = 7

replace [cos(x)=t] and extender with-1

4tē-8t-4 = -7 <--> t1= 1/2 t2=3/2

cos(x1)=1/2

cos(x2)=3/2

then you get the first x but the other ?