सिद्ध कीजिए -
`sin^(-1).(4)/(5)+sin^(-1).(5)/(13)+sin^(-1).(16)/(65)=(pi)/(2).`

Explanation

L.H.S. `=sin^(-1).(4)/(5)+sin^(-1).(5)/(13)+sin^(-1).(16)/(65)`
`=sin^(-1)[(4)/(5)xxsqrt(1-((5)/(13))^(2))+(5)/(13)xxsqrt(1-((4)/(5))^(2))]+sin^(-1).(16)/(65)`
`=sin^(-1)[(4)/(5)xxsqrt((144)/(169))+(5)/(13)xx sqrt((9)/(25))]+sin^(-1).(16)/(65)`
`=sin^(-1)((4)/(5)xx(12)/(13)+(5)/(13)xx(3)/(5))+sin^(-1).(16)/(65)`
`=sin^(-1)((45)/(65)+(15)/(65))+sin^(-1).(16)/(65)`
`=sin^(-1)((63)/(65))+sin^(-1)((16)/(65))`
`=sin^(-1)[(63)/(65)sqrt(1-((16)/(65))^(2))+(16)/(65)sqrt(1-((63)/(65))^(2))]`
`=sin^(-1)[(63)/(65)sqrt((4225-256)/(4225))+(16)/(65)xxsqrt((4225-3969)/(4225))]`
`=sin^(-1)[(63)/(65)xxsqrt((3969)/(4225))+(16)/(65)xx sqrt((256)/(4225))]`
`=sin^(-1)[(63)/(65)xx(63)/(65)+(16)/(65)xx(16)/(65)]`
`=sin^(-1)((3969+256)/(4225))`
`=sin^(-1)((4225)/(4225))`
`=sin^(-1)=(pi)/(2)`
= R.H.S.
यही सिद्ध करना था।