If `y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)},` find `(dy)/(dx).`

Options

A. `(1)/(sqrt( 1 - x^(2))) `
B. `-(1)/(sqrt( 1 - x^(2))) `
C. `(3)/(sqrt( 1 - x^(2))) `
D. None of these

Answer

A

Explanation

On Putting ` x = sin theta , 5 = r cos alpha " and " 12 = r sin alpha` , we get
`y = sin^(-1) ((r cos alpha sin theta + r sin alpha cos theta )/(13))`
` = sin^(-1) ((13 sin (theta + alpha))/(13))" " [ because = 13] `
` = (theta + alpha ) = sin^(-1) x + tan^(-1) ""(12)/(5) `
` therefore (dy)/(dx) = (1)/(sqrt( 1 - x^(2)))`