$\cot \left({\tan }^{-1}x+{\cot }^{-1}x\right)=?$

Mark the tick against the correct answer in the following:

${\tan }^{-1}1+{\tan }^{-1}\frac{1}{3}=?$

Mark the tick against the correct answer in the following:

${\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{1}{3}=?$

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$2{\tan }^{-1}\frac{1}{3}=?$

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$\cos \left(2{\tan }^{-1}\frac{1}{2}\right)=?$

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$\sin \left(2{\tan }^{-1}\frac{5}{8}\right)=?$

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$\sin \left(2{\sin }^{-1}\frac{4}{5}\right)=?$

Mark the tick against the correct answer in the following:

If ${\tan }^{-1}x=\frac{\mathrm{\pi }}{4}-{\tan }^{-1}\frac{1}{3}$ then $x=?$

Mark the tick against the correct answer in the following:

If ${\tan }^{-1}\left(1+x\right)+{\tan }^{-1}\left(1-x\right)=\frac{\mathrm{\pi }}{2}$ then $x=?$