Let's find the value of each term first:

cos(a+b) + cos(a-b) = 2cos(a)cos(b)cos(a-b) - cos(a+b) = -2sin(a)sin(b)ctg(a) = cos(a) / sin(a)

Now, let's substitute these values into the given equation:

(2cos(a)cos(b)) / (-2sin(a)sin(b)) = (-cos(a)sin(a)) / (cos(a)sin(a))

Simplify the equation:

-tan(a)tan(b) = -1

Therefore, ctg(a)*ctg(b) = 1