If `A = int_(1)^(sintheta) (t)/(1 + r^(2)) dt and B = int_(1)^("cosec"theta) (1)/(t(1 +t^(2))) dt`, then the value of the determinant
`|(A,A^(2),B),(e^(A +B),B^(2),-1),(1,A^(2) + B^(2) ,-1)|` is

Explanation

To solve the given problem, we need to evaluate the determinant:

\[
D = \begin{vmatrix}
A & A^2 & B \\
e^{A+B} & B^2 & -1 \\
1 & A^2 + B^2 & -1
\end{vmatrix}
...