Question

If   `y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))),` then show that `dy/dx=cosx/(2y-1)`

Answer 1

`y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo)))`

Let  `y=sqrt(sinx+y)`

`y^2=sinx+y `

Differentiat ing w.r.t.x,

`2y.dy/dx=cosx+dy/dx`

`dy/dx=cosx/(2y-1)`