$\sin ^{-1}\left(\frac{3}{5}\right)-\sin ^{-1}\left(\frac{8}{17}\right)=$ . . . . . .

$\sin \left[\tan ^{-1}\left(\frac{1-x^2}{2 x}\right)+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right]$ ની કિંમત શોધો.

$\tan \left(2 \tan ^{-1}\left(\frac{\sqrt{5}-1}{2}\right)\right)$ નું મૂલ્ય શોધો.

અસમતા $\cos ^{-1} x < \sin ^{-1} x$ નો ઉકેલ ગણ શું છે?

$\sin ^{-1}\left(\cos \frac{\pi}{13}\right)+\cos ^{-1}\left(\sin \frac{\pi}{13}\right) = $ . . . . . . .

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