14. Inverse Trigonometric Functions question bank (Maths)

All possible values of \( p \) and \( q \) for which
\(
\cos^{-1} \sqrt{p} + \cos^{-1} \sqrt{1 - p} + \cos^{-1} \sqrt{1 - q} = \frac{3\pi}{4}
\)
holds, is

\(\frac{a^3}{2} \csc^2\left(\frac{1}{2} \tan^{-1} \frac{a}{b}\right) + \frac{b^3}{2} \sec^2 \left(\frac{1}{2} \tan^{-1} \frac{b}{a}\right)\) is equal to