Evaluate the limit of expression 4cosx-6sin^2x+3tan^2x. x-->x0 , x0=60 degrees

To evaluate the limit, we'll have to substitute x by the
value of x0, in the given expression.

lim
(4cosx-6sin^2x+3tan^2x) = 4cos 60 - 6*(sin 60)^2 + 3*(tan
60)^2

cos 60 = 1/2

sin 60 =
sqrt3/2

We'll raise to square both
sides:

(sin 60)^2 =
(sqrt3/2)^2

(sin 60)^2 =
3/4

tan 60 = sqrt 3

We'll
raise to square both sides:

(tan 60)^2 =
3

We'll substitute the values of the functions in the
expresison above:

lim (4cosx-6sin^2x+3tan^2x) = 4(1/2) -
6*(3/4) + 3*(3)

lim (4cosx-6sin^2x+3tan^2x) = 2 - 9/2 +
9

lim (4cosx-6sin^2x+3tan^2x) = (4 - 9 +
18)/2

lim (4cosx-6sin^2x+3tan^2x) = 13/2, for
x-> 60 degrees