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If e^((sin^(2)x+sin^(4)x+…+"ad inf.")log...

If `e^((sin^(2)x+sin^(4)x+…+"ad inf.")log_(e )2), (0 lt x lt pi//2)`, satisfies `y^(2)-5y+4=0`, then `(sinx)/(cosx-sinx)` is equal to

A

`-(2+sqrt(2))`

B

`-(sqrt(2)+1)`

C

`sqrt(2)-1`

D

`2+sqrt(2)`

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