^ - 1 ( 15 17 ) + 2 ^ - 1 ( 1 5 ) = - Vidyadip

MCQ

${\cos ^{ - 1}}\left( {\frac{{15}}{{17}}} \right) + 2{\tan ^{ - 1}}\left( {\frac{1}{5}} \right) = $

A
$\frac{\pi }{2}$
B
${\cos ^{ - 1}}\left( {\frac{{171}}{{221}}} \right)$
C
$\frac{\pi }{4}$
✓
એકપણ નહીં.

✓

Answer

Correct option: D.

એકપણ નહીં.

${\cos ^{ - 1}}\left( {\frac{{15}}{{17}}} \right) + 2{\tan ^{ - 1}}\left( {\frac{1}{5}} \right)$
$ = {\cos ^{ - 1}}\left( {\frac{{15}}{{17}}} \right) + {\cos ^{ - 1}}\left( {\frac{{1 - 1/25}}{{1 + 1/25}}} \right)$
$ = {\cos ^{ - 1}}\left( {\frac{{15}}{{17}}} \right) + {\cos ^{ - 1}}\left( {\frac{{12}}{{13}}} \right)$
$ = {\cos ^{ - 1}}\left( {\frac{{15}}{{17}} \times \frac{{12}}{{13}} - \sqrt {1 - {{\left( {\frac{{15}}{{17}}} \right)}^2}} \sqrt {1 - {{\left( {\frac{{12}}{{13}}} \right)}^2}} } \right)$
$ = {\cos ^{ - 1}}\left( {\frac{{140}}{{221}}} \right)$.

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