B)
c)1
d) -1

Solution:
We can simplify the given expression using the identity:
tan(A + B) = (tanA + tanB)/(1- tanAtanB)

Therefore,
(tanA tanB)/(1- tanAtanB) = tanA tanB / (tan(A+B))

Now, we can see that the numerator is the product of two tangents, which suggests that we should consider the formula for tangent of sum of two angles.

tan(A+B) = (tanA + tanB)/(1- tanAtanB)

Rearranging the terms, we get:

tanA+ tanB = tan(A+B) (1- tanAtanB)

Substituting this in the expression we got earlier, we get:

(tanA tanB)/(1- tanAtanB) = tanA tanB / (tanA + tanB)

Now, we can use the formula for tangent of difference of two angles to simplify the denominator:

tan(A-B) = (tanA - tanB)/(1+ tanAtanB)

Rearranging the terms, we get:

tanA - tanB = tan(A-B) (1+ tanAtanB)

Adding and subtracting the two equations we got earlier, we get:

2tanA = tan(A+B) (1- tanAtanB) + tan(A-B) (1+ tanAtanB)
2tanB = tan(A+B) (1- tanAtanB) - tan(A-B) (1+ tanAtanB)

Dividing the first equation by the second, we get:

tanA/tanB = (tan(A+B) (1- tanAtanB) + tan(A-B) (1+ tanAtanB)) / (tan(A+B) (1- tanAtanB) - tan(A-B) (1+ tanAtanB))

Simplifying this expression, we get:

tanA/tanB = (tan(A+B) + tan(A-B)) / (1 - tan^2(A-B))

Using the formula for tangent of sum of two angles and simplifying further, we get:

tanA/tanB = tan(2A) / (1 - tan^2B)

Multiplying both sides by tanB and simplifying, we get:

tanA = tan(2A) tanB

Therefore, the answer is (a) tan(A-B).