1) 4sin^2 x - 11cos x - 11 = 0
Rearranging the equation using the identity sin^2 x + cos^2 x = 1:
4(1 - cos^2 x) - 11cos x - 11 = 0
4cos^2 x - 11cos x - 7 = 0

2) 4sin^2 x + 9sin x cos x + 2cos^2 x = 0
Rearranging the equation using the identity sin^2 x + cos^2 x = 1:
4(1 - cos^2 x) + 9sin x cos x + 2cos^2 x = 0
4cos^2 x + 9sin x cos x + 6 = 0

3) 3tg x - 8ctg x + 10 = 0
Replacing cotangent with tangent:
3tan x - 8tan x + 10 = 0
-5tan x + 10 = 0

4) 3sin(2x) + 8sin^2(x) = 7
Using the double angle formula for sine:
6sin x cos x + 8sin^2 x = 7
Rearranging:
8sin^2 x + 6sin x cos x - 7 = 0