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Prove the following: cos^(-1)((12)/(13)...

Prove the following: `cos^(-1)((12)/(13))+sin^(-1)(3/5)=sin^(-1)((56)/(65))`

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LHS `=cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)`
`=sin^(-1)sqrt(1-((12)/(13))^(2))+sin^(-1)""(3)/(5)" " ( :. cos^(-1)x=sin^(-1)sqrt(1-x^(2)))`
`=sin^(-1)""(5)/(13)+sin^(-1)""(3)/(5)`
`=sin^(-1)[(5)/(13)sqrt(1-((3)/(5))^(2))+(3)/(5)sqrt(1-((5)/(13))^(2))]`
`sin^(-1)[(5)/(13)xx(4)/(5)+(3)/(5)xx(12)/(13)]`
`=sin^(-1)""(56)/(65)=` RHS. Hence Proved.
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