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Sin^(-1)((12)/(13))-sin^(-1)((3)/(5)) is...

`Sin^(-1)((12)/(13))-sin^(-1)((3)/(5))` is equal to

A

`(pi)/(2)-cos^(-1)((9)/(65))`

B

`pi-cos^(-1)((33)/(65))`

C

`(pi)/(2)-sin^(-1)((56)/(65))`

D

`pi-sin^(-1)((63)/(65))`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin.(sqrt2)/(sqrt3)-sin^(-1).(3)/(5)`
`=cos^(-1).(5)/(13)-cos^(-1).(4)/(5)=cos^(-1)[(5)/(13).(4)/(5)+(12)/(13).(3)/(5)]-((5)/(13)lt(4)/(5))=cos^(-1)[(56)/(65)]=(pi)/(2)-sin^(-1).(56)/(65)`
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