JEE MAIN - Mathematics (2019 - 12th April Morning Slot - No. 9)
The value of $${\sin ^{ - 1}}\left( {{{12} \over {13}}} \right) - {\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ is equal to :
$$\pi - {\sin ^{ - 1}}\left( {{{63} \over {65}}} \right)$$
$${\pi \over 2} - {\sin ^{ - 1}}\left( {{{56} \over {65}}} \right)$$
$${\pi \over 2} - {\cos ^{ - 1}}\left( {{9 \over {65}}} \right)$$
$$\pi - {\cos ^{ - 1}}\left( {{{33} \over {65}}} \right)$$
Explanation
$${\sin ^{ - 1}}{{12} \over {13}} - {\sin ^{ - 1}}{3 \over 5} = {\sin ^{ - 1}}\left( {{{12} \over {13}}.{4 \over 5}.{3 \over 5}.{5 \over {13}}} \right)$$
$$ \Rightarrow {\sin ^{ - 1}}{{33} \over {65}} = {\pi \over 2} - {\cos ^{ - 1}}{{33} \over {65}}$$
$$ \Rightarrow {\pi \over 2} - {\sin ^{ - 1}}{{56} \over {65}}$$
$$ \Rightarrow {\sin ^{ - 1}}{{33} \over {65}} = {\pi \over 2} - {\cos ^{ - 1}}{{33} \over {65}}$$
$$ \Rightarrow {\pi \over 2} - {\sin ^{ - 1}}{{56} \over {65}}$$
Comments (0)
