Determine whether the equation is an identity. If it is an identity, prove it.-(2 sin x + cos x)2 - (2 cos x - sin x)2 = -5

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The statement is an identity.
-(2 sin x + cos x)2 - (2 cos x - sin x)2 =
-(4 sin2 x + 4 sin x cos x + cos2 x) - (4 cos2 x - 4 sin x cos x + sin2 x) = 
-4 sin2 x - 4 sin x cos x - cos2 x - 4 cos2 x + 4 sin x cos x - sin2 x = 
-4 sin2 x - cos2 x - 4 cos2 x - sin2 x = -(4 sin2 x + 4 cos2 x + sin2 x + cos2 x) =
-(4(sin2 x + cos2 x) + 1) = -(4 + 1) = -5

Mathematics

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