Question
$4\, {\tan ^{ - 1}}\frac{1}{5} - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}} = $
$ = 2\, {\tan ^{ - 1}}\left[ {\frac{{\frac{2}{5}}}{{1 - \frac{1}{{25}}}}} \right] - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}}$
$ = 2\, {\tan ^{ - 1}}\left( {\frac{5}{{12}}} \right) - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}}$
$ = {\tan ^{ - 1}}\left[ {\frac{{\frac{5}{6}}}{{1 - \frac{{25}}{{144}}}}} \right] - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}}$
$ = {\tan ^{ - 1}}\left( {\frac{{120}}{{119}}} \right) - {\tan ^{ - 1}}\frac{1}{{70}} + {\tan ^{ - 1}}\frac{1}{{99}}$
$ = {\tan ^{ - 1}}\left( {\frac{{120}}{{119}}} \right) + {\tan ^{ - 1}}\left[ {\frac{{\frac{1}{{99}} - \frac{1}{{70}}}}{{1 + \frac{1}{{99}}.\frac{1}{{70}}}}} \right]$
$ = {\tan ^{ - 1}}\left( {\frac{{120}}{{119}}} \right) + {\tan ^{ - 1}}\left( {\frac{{ - 29}}{{6931}}} \right)$
$ = {\tan ^{ - 1}}\frac{{120}}{{119}} - {\tan ^{ - 1}}\frac{{29}}{{6931}} = {\tan ^{ - 1}}\frac{{120}}{{119}} - {\tan ^{ - 1}}\frac{1}{{239}}$
$ = {\tan ^{ - 1}}\left[ {\frac{{\frac{{120}}{{119}} - \frac{1}{{239}}}}{{1 + \frac{{120}}{{119}} \times \frac{1}{{239}}}}} \right] $
$= {\tan ^{ - 1}}(1) = \frac{\pi }{4}$.
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$I$. $4,{ }^x$ को विभाजित करता है या $4, y$ को विभाजित करता है।
$II$. $3,{ }^{x+y}$ को विभाजित करता है या $3, x-y$ को विभाजित करता है।
$III$. $5,2\left(x^2-y^2\right)$ को विभाजित करता है।
$\left[\begin{array}{ll}4 & 3 \\ x & 5\end{array}\right]=\left[\begin{array}{ll}y & z \\ 1 & 5\end{array}\right]$