We have to find the value of lim x--> 60 degrees[ 4cos x - 6(sin x)^2 + 3*tan x)^2]
Here we see that cos 60 , (sin 60)^2 and (tan 60)^2 are defined, so we can just substitute x with 60.
Substituting x = 60 degrees
4cos x - 6(sin x)^2 + 3*tan x)^2
=> 2 - 6*(3/4) + 3* 3
=> 2 - 4.5 + 9
=> 6.5
The required value of lim x--> 60 degrees[ 4cosx - 6sin^2x + 3tan^2x] is 6.5