To simplify the given expression, let's start by simplifying each term separately.

Simplifying (cos12° - sin12°)/(cos12° sin12°):
We can rewrite the numerator using the trigonometric identity for the difference of angles: cos(A - B) = cos A cos B + sin A sin B.
So, cos12° - sin12° = cos(45° - 33°) = cos45° cos33° + sin45° sin33°.
Since cos45° = sin45° = 1/√2, we have:
cos12° - sin12° = (1/√2)(cos33° + sin33°).

Now let's simplify the denominator cos12° sin12°:
Using the double angle formula for sin2A = 2sinAcosA, we can rewrite sin12° as 2sin6°cos6°.
So, cos12° sin12° = cos12°(2sin6°cos6°) = 2cos12°sin6°cos6°.

Now we can rewrite the given expression as:
[(cos12° - sin12°)/(cos12° sin12°)] / [sin147° / cos147°].

Simplifying the numerator:
(cos12° - sin12°)/(cos12° sin12°) = (1/√2)(cos33° + sin33°) / (2cos12°sin6°cos6°).
We can rewrite sin33° using the double angle formula sin2A = 2sinAcosA:
(1/√2)(cos33° + sin33°) = (1/√2)(cos33° + 2sin16°cos16°).

Simplifying the denominator:
sin147° / cos147° = sin33° / cos33°.
Using the double angle formula sin2A = 2sinAcosA, we can rewrite sin33° as 2sin16°cos16°.

Now we can rewrite the expression as:
[(1/√2)(cos33° + 2sin16°cos16°)] / [(2sin16°cos16°) / cos33°].

Canceling out common terms, we get:
(1/√2)(cos33° + 2sin16°cos16°) / (2sin16°) = (1/√2)(cos33°/sin16° + 2cos16°) / (2sin16°).
Simplifying further, we have:
(1/√2)(cot16°cos33° + 2cos16°) / (2sin16°).

Since cotθ = 1/tanθ, we can rewrite cot16° as 1/tan16°:
(1/√2)((1/tan16°)cos33° + 2cos16°) / (2sin16°).

Now we can simplify the expression further:
(1/√2)((cos33° + 2tan16°cos16°) / (2sin16°tan16°)).

Using the trigonometric identity sinθ/cosθ = tanθ, we can rewrite the expression as:
(1/√2)((cos33° + 2tan16°cos16°) /