1.

सिद्ध कीजिए कि - `(9pi)/(8)-(9)/(4)sin^(-1)((1)/(3))=(9)/(4)sin^(-1)((2sqrt2)/(3)).`

Answer» `L.H.S.=(9pi)/(8)-(9)/(4)sin^(-1)((1)/(3))`
`=(9)/(4)[(pi)/(2)-sin^(-1)((1)/(3))]`
`=(9)/(4)[cos^(-1)((1)/(3))]," "[because sin^(-1)x+cos^(-1)x=(pi)/(2)]`
`=(9)/(4)sin^(-1)(sqrt(1-(1)/(9)))," "[because cos^(-1)x=sin^(-1)sqrt(1-x^(2))]`
`=(9)/(4)sin^(-1)(sqrt((8)/(9)))`
`=(9)/(4)sin^(-1)((2sqrt2)/(3))`
= R.H.S.`" "` यही सिद्ध करना था ।


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