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If y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dot...

If `y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dotto\ oo)))` , prove that `(dy)/(dx)=(s e c^2x)/(2y-1)`

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Verified by Experts

Given that,
`y=sqrt(tanx+sqrt(tanx+sqrt(tanx+\ dotto\ oo)))`
`y=sqrt(tanx+y)`
`=>y^2=tanx+y`
`=>y^2-y=tanx`
`=>d/(dx)(y^2-y)=d/(dx)tanx`
`=>(2y-1)(dy)/(dx)=sec^2x`
`=>(dy)/(dx)=sec^2x/(2y-1)`
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