The value of ^ - 1 , ( 12 13 ) - ^ - 1 , ( 3 5 ) is equal to - Vidyadip

MCQ

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

A
$\pi - {\cos ^{ - 1}}\,\left( {\frac{{33}}{{65}}} \right)$
B
$\pi - {\sin ^{ - 1}}\,\left( {\frac{{63}}{{65}}} \right)$
C
$\frac{\pi }{2} - {\cos ^{ - 1}}\,\left( {\frac{9}{{65}}} \right)$
✓
$\frac{\pi }{2} - {\sin ^{ - 1}}\,\left( {\frac{56}{{65}}} \right)$

✓

Answer

Correct option: D.

$\frac{\pi }{2} - {\sin ^{ - 1}}\,\left( {\frac{56}{{65}}} \right)$

d
${\sin ^{ - 1}}\left( {\frac{{12}}{{13}}} \right) - {\sin ^{ - 1}}\left( {\frac{3}{5}} \right)$

${\sin ^{ - 1}}\left( {x\sqrt {1 - {y^2}} - y\sqrt {1 - {x^2}} } \right)$

$ = {\sin ^1}\left( {\frac{{33}}{{65}}} \right) = {\cos ^{ - 1}}\left( {\frac{{56}}{{65}}} \right) = \frac{\pi }{2} - {\sin ^{ - 1}}\left( {\frac{{56}}{{65}}} \right)$

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