The value of [ ^ - 1( 12 13 ) - ^ - 1( 3 5 )] is equal to :

Question

The value of $${\sin ^{ - 1}}\left( {{{12} \over {13}}} \right) - {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ is equal to :

Accepted Answer

$${\sin ^{ - 1}}{{12} \over {13}} - {\sin ^{ - 1}}{3 \over 5} = {\sin ^{ - 1}}\left( {{{12} \over {13}}.{4 \over 5}.{3 \over 5}.{5 \over {13}}} \right)$$

$$ \Rightarrow {\sin ^{ - 1}}{{33} \over {65}} = {\pi  \over 2} - {\cos ^{ - 1}}{{33} \over {65}}$$

$$ \Rightarrow {\pi  \over 2} - {\sin ^{ - 1}}{{56} \over {65}}$$

Solutions · 1