(2sin^2a-1)/(1-2cos2a)

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To simplify this expression, we need to first use the double angle identity for cosine:

cos(2a) = 2cos^2(a) - 1

So, we can rewrite the expression as:

(2sin^2(a) - 1) / (1 - 2cos(2a))

Substitute the double angle identity:

(2sin^2(a) - 1) / (1 - 2(2cos^2(a) - 1))

Expand and simplify the denominator:

(2sin^2(a) - 1) / (1 - 4cos^2(a) + 2)

Simplify further:

(2sin^2(a) - 1) / (3 - 4cos^2(a))

Now, we can simplify this expression further if needed based on the context provided or given conditions. Let me know if you need further assistance.