Questions in inv-trig

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If $\sin \left( {{\sin }^{-1}}\frac{1}{5}+{{\cos }^{-1}}x \right)=1$,then x is equal to
If ${{\sin }^{-1}}x=\theta +\beta $and ${{\sin }^{-1}}y=\theta -\beta ,$then $1+xy=$
If ${{\sin }^{-1}}\frac{1}{3}+{{\sin }^{-1}}\frac{2}{3}={{\sin }^{-1}}x,$then x is equal to
$\tan ({{\cos }^{-1}}x)$ is equal to
The domain of ${{\sin }^{-1}}x$is
The principal value of ${{\sin }^{-1}}\left( -\,\,\frac{\sqrt{3}}{2} \right)$is
$\cot \,\,\left[ {{\cos }^{-1}}\left( \frac{7}{25} \right) \right]=$
If $\frac{\pi }{2}\le x\le \frac{3\pi }{2},$then${{\sin }^{-1}}(\sin x)$is equal to
If $\pi \le x\le 2\pi $, then ${{\cos }^{-1}}(\cos x)$is equal to
The value of ${{\sin }^{-1}}(\sin 10)$is

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