Given that 2 tan x = sec x
i.e. 2 * sin x / cos x = 1 / cos x
Assuming cos x is not 0, (in which case tan x would be infinity) we can cancel
out the 2 cos x's in the denominators to get the equation
2 * sin x = 1
or sin x = 1/2
Now the other ratios can be computed.
cos x = sqrt(1 - sin^2 x) = sqrt (1 - 1/4) =  (+ or -)
tan x = sin x / cos x =  (+ or -)
cot x = 1 / tan x =  (+ or -)

Now, the given exp is 4*cot^2 x - 8 * tan^2 x
= 

Hope this helps :)