Simplify: \(\dfrac{\sin^2A}{1-\cos A} + \dfrac{\sin^2A}{1+\cos A}\)
2
Combine the two fractions over a common denominator: \(\dfrac{\sin^2A(1+\cos A)+\sin^2A(1-\cos A)}{(1-\cos A)(1+\cos A)}\).
The numerator simplifies to \(\sin^2A\times2 = 2\sin^2A\), and the denominator to \(1-\cos^2A = \sin^2A\) (using the Pythagorean identity).
So the expression becomes \(\dfrac{2\sin^2A}{\sin^2A} = 2\).
Hence, the simplified value is 2.
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