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If exp[sin^(2)x+sin^(4)x+sin^(6)x+….inft...

If exp`[sin^(2)x+sin^(4)x+sin^(6)x+….infty)ln 2]` satisfies the equation `y^(2)-9y+8=0` and the value of `(cosx)/(cos x+sin x),0 lt x lt (pi)/(2)` is `(1)/(1+sqrt(k))` then the value of k is _________

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