`=>` Key in what to substitute:
`sin^(-1) (x) =theta`
`x= sin theta`
`cos theta= sqrt (1-x^2)`
`theta= cos^(-1) sqrt(1-x^2)`
`theta= cos^(-1) sqrt(1-x^2)`
`tan theta= x/(sqrt(1-x^2))`
`=> theta=tan^(-1) \ x/(sqrt(1- x^2))`
`sin^(-1) (tan^(-1) \ 1/7)`
`tan^(-1) \ 1/7 = theta`
`tan \ theta = 1/7`
`=> sin theta= 1/(sqrt 50)`
`=> theta= sin^(-1) \ 1/(sqrt (50))`
`=> sin \ (tan ^(-1) \ 1/7) = sin \ sin^(-1) \ 1/(sqrt (50))`
`= 1/(sqrt (50))`
`=>` Key in what to substitute:
`sin^(-1) (x) =theta`
`x= sin theta`
`cos theta= sqrt (1-x^2)`
`theta= cos^(-1) sqrt(1-x^2)`
`theta= cos^(-1) sqrt(1-x^2)`
`tan theta= x/(sqrt(1-x^2))`
`=> theta=tan^(-1) \ x/(sqrt(1- x^2))`
`sin^(-1) (tan^(-1) \ 1/7)`
`tan^(-1) \ 1/7 = theta`
`tan \ theta = 1/7`
`=> sin theta= 1/(sqrt 50)`
`=> theta= sin^(-1) \ 1/(sqrt (50))`
`=> sin \ (tan ^(-1) \ 1/7) = sin \ sin^(-1) \ 1/(sqrt (50))`
`= 1/(sqrt (50))`