If `0ltxlt(pi)/(2)` exp `[(sin^(2)x+sin^(4)x+sin^(6)x+'.....+oo)log_(e)2]` satisfies the quadratic equation `x^(2)-9x+8=0`, find the value of `(sinx-cosx)/(sinx+cosx)`.

Explanation

To solve the problem step by step, we start with the given expression and the quadratic equation.

### Step 1: Understanding the Series
The series given is:
\[ \sin^2 x + \sin^4 x + \sin^6 x + \ldots \]
This is an infinite geometric series where the first term \(a = \sin^2 x\) and the common ratio \(r = \sin^2 x\).
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