$\sec ^2(\tan ^{-1} 2)+\operatorname{cosec}^2(\cot ^{-1} 3) = $

જો $\sin ^{-1} x - \cos ^{-1} x = \frac{\pi}{6}$ હોય, તો $x$ ની કિંમત શોધો.

જો $3 \cos ^{-1} x + \sin ^{-1} x = \pi$ હોય,તો $x = $ . . . . . . .

$2 \tan^{-1}(\cos x) = \tan^{-1}(\csc^2 x)$ હોય,તો $x = $

જો $\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\cdots+\tan ^{-1}\left[\frac{1}{1+n(n+1)}\right]=\tan ^{-1}[x]$ હોય,તો $x=$

$\tan \left[ {\frac{\pi }{4} + \frac{1}{2}{{\cos }^{ - 1}}\frac{a}{b}} \right] + \tan \left[ {\frac{\pi }{4} - \frac{1}{2}{{\cos }^{ - 1}}\frac{a}{b}} \right] = $