$\cot ^{ - 1}\left[ \frac{\sqrt {1 - \sin x} + \sqrt {1 + \sin x}}{\sqrt {1 - \sin x} - \sqrt {1 + \sin x}} \right] = $

यदि $2 \sin ^{-1} x-3 \cos ^{-1} x=4, x \in[-1,1]$ है,तो $2 \sin ^{-1} x+3 \cos ^{-1} x$ का मान ज्ञात कीजिए।

कथन-$1$: ${\cot ^{ - 1}}\left[ {\frac{{\log (e/{x^2})}}{{\log (ex^2)}}} \right] + {\cot ^{ - 1}}\left[ {\frac{{\log (ex^2)}}{{\log (e/{x^2})}}} \right] = \frac{\pi}{2}$
कथन-$2$: ${\tan ^{ - 1}}\left[ {\frac{{1 + \log {x^2}}}{{1 - \log {x^2}}}} \right] = {\tan ^{ - 1}}1 + {\tan ^{ - 1}}(\log {x^2})$

यदि $\cos ^{-1} 2x + \cos ^{-1} 3x = \frac{\pi}{3}$ है, तो $x =$

$2{\sin ^{ - 1}}\frac{3}{5} + {\cos ^{ - 1}}\frac{{24}}{{25}} = $

यदि $4 \cos^{-1} x + \sin^{-1} x = \frac{\pi}{2}$ है,तो $x =$ . . . . . . .