To find the value of 2cot(P-A/2) / 1 - tan^2(2P-A/2), we can start by simplifying each term step by step.

Step 1: Simplify cot(P-A/2)
We know that cot(P-A/2) = cos(P-A/2) / sin(P-A/2).
Using the angle difference formula, we have:
cos(P-A/2) = cosP*cos(A/2) + sinP*sin(A/2)
sin(P-A/2) = sinP*cos(A/2) - cosP*sin(A/2)
So, cot(P-A/2) = (cosP*cos(A/2) + sinP*sin(A/2)) / (sinP*cos(A/2) - cosP*sin(A/2))

Step 2: Simplify tan(2P-A/2)
Using the double-angle formula for tangent, we have:
tan(2P-A/2) = (2*tanP) / (1 - tan^2P)
Since tanP = sinP / cosP, we can substitute this value into the equation:
tan(2P-A/2) = (2*sinP / cosP) / (1 - (sinP / cosP)^2)
tan(2P-A/2) = (2*sinP / cosP) / (1 - sin^2P / cos^2P)
tan(2P-A/2) = (2*sinP / cosP) / (cos^2P - sin^2P) / cos^2P
tan(2P-A/2) = (2*sinP / cosP) * (cos^2P / (cos^2P - sin^2P))

Step 3: Simplify the expression
Substituting the values from step 1 and step 2 into the expression 2cot(P-A/2) / 1 - tan^2(2P-A/2), we get:
(2*(cosP*cos(A/2) + sinP*sin(A/2)) / (sinP*cos(A/2) - cosP*sin(A/2))) / (1 - (2*sinP / cosP) * (cos^2P / (cos^2P - sin^2P)))

Next, we can simplify the numerator and denominator separately.

Numerator:
2*(cosP*cos(A/2) + sinP*sin(A/2))
= 2*cosP*cos(A/2) + 2*sinP*sin(A/2)

Denominator:
1 - (2*sinP / cosP) * (cos^2P / (cos^2P - sin^2P))
= 1 - (2*sinP * cos^2P) / (cosP * (cos^2P - sin^2P))
= 1 - 2*sinP*cosP / (cos^2P - sin^2P)

Now, substituting the simplified numerator and denominator back into the expression, we have:
(2*cosP*cos(A/2) + 2*sinP*sin(A/2)) / (1 - 2*sinP*cosP / (cos^2P - sin^2P))

Finally, we can factor out a 2 from both terms in the numerator:
2 * (cosP*cos(A/2