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

  • Option 1)

    \frac{\pi }{2}-\cos ^{-1}\left ( \frac{9}{65} \right )

  • Option 2)

    \pi -\sin ^{-1}\left ( \frac{63}{65} \right )

  • Option 3)

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

     

  • Option 4)

    \pi -\cos ^{-1}\left ( \frac{33}{65} \right )

 

Answers (1)

 

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

=\tan ^{-1}\left ( \frac{12}{5} \right )-\tan ^{-1}\left ( \frac{3}{4} \right )

=\tan ^{-1}\left ( \frac{\frac{12}{5}-\frac{3}{4}}{1+\frac{12}{5}\times \frac{3}{4}} \right )

=\tan ^{-1}\left ( \frac{\frac{48-15}{20}}{\frac{20+36}{20}} \right )

=\tan ^{-1}\left ( \frac{33}{56} \right )

=\cos ^{-1}\left ( \frac{56}{65} \right )

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


Option 1)

\frac{\pi }{2}-\cos ^{-1}\left ( \frac{9}{65} \right )

Option 2)

\pi -\sin ^{-1}\left ( \frac{63}{65} \right )

Option 3)

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

 

Option 4)

\pi -\cos ^{-1}\left ( \frac{33}{65} \right )

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Vakul

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