Which expression is equivalent to 4 sine squared x minus 8 sine squared open paren x over 2 close paren ?

Use the half-angle identity sin²(x/2) = (1 − cos x)/2 and the identity sin²x = 1 − cos²x. Substituting gives 4(1 − cos²x) − 4(1 − cos x) = 4(cos x − cos²x). This matches choice A: 4 times (cosine of x minus cosine squared of x).

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