If A=∫sinθ1t dt1+t2dt,B=∫cosecθ11t(1+t2)dt then ∣∣∣∣∣AA2BeA+BB2−11A2+B2−1∣∣∣∣∣=?

If A=∫sinθ1t dt1+t2dt,B=∫cosecθ11t(1+t2)dt then ∣∣∣∣∣A

1.	If A=∫sinθ1t dt1+t2dt,B=∫cosecθ11t(1+t2)dt then ∣∣∣∣∣AA2BeA+BB2−11A2+B2−1∣∣∣∣∣=?
Answer» If $A = \int_{1}^{s i n θ} \frac{t d t}{1 + t^{2}} d t, B = \int_{1}^{c o s e c θ} \frac{1}{t (1 + t^{2})} d t$ then $∣ ∣∣∣ ∣ \begin{matrix} A & A^{2} & B e^{A + B} & B^{2} & - 1 1 & A^{2} + B^{2} & - 1 \end{matrix} ∣ ∣∣∣ ∣ = ?$