MCQ
${\cos ^{ - 1}}\frac{4}{5} + {\tan ^{ - 1}}\frac{3}{5} = $
- ✓${\tan ^{ - 1}}\frac{{27}}{{11}}$
- B${\sin ^{ - 1}}\frac{{11}}{{27}}$
- C${\cos ^{ - 1}}\frac{{11}}{{27}}$
- DNone of these
$= {\tan ^{ - 1}}\left[ {\frac{{\sqrt {\left( {1 - \frac{{16}}{{25}}} \right)} }}{{\frac{4}{5}}}} \right] + {\tan ^{ - 1}}\frac{3}{5}$
$\left[ {{\rm{Since}}\,\,{{\cos }^{ - 1}}x = {{\tan }^{ - 1}}\frac{{\sqrt {(1 - {x^2})} }}{x}} \right]$
$ = {\tan ^{ - 1}}\frac{3}{4} + {\tan ^{ - 1}}\frac{3}{5} $
$= {\tan ^{ - 1}}\,\left( {\frac{{\frac{3}{4} + \frac{3}{5}}}{{1 - \frac{3}{4}.\frac{3}{5}}}} \right) = {\tan ^{ - 1}}\left( {\frac{{27}}{{11}}} \right)$.
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