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If `sin(sin^(-1)1/5+cos^(-1)x)=1,` then find the value of `xdot`

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If `sin(sin^(-1)1/5+cos^(-1)x)=1,` then find the value of `xdot`
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`sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1`
`implies sin (sin^(-1)""(1)/(5)+cos^(-1)x)=sin""(pi)/(2)`
`implies sin^(-1)""(1)/(5)+cos^(-1)x=(pi)/(2)`
`implies sin^(-1)""(1)/(5)=(pi)/(2)-cos^(-1)x`
`implies sin^(-1)""(1)/(5)=sin^(-1)ximplies x=(1)/(5)`
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