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Let M and m respectively be the maximum and the minimum values of f(x) = | 1+sin^2 x cos^2 x 4sin 4x | | sin^2 x 1+cos^2 x 4sin 4x |, x ∈ R | sin^2 x cos^2 x 1+4sin 4x |. Then M^4 − m^4 is equal to :

1. 1280
2. 1295
3. 1040
4. 1215

Correct answer: 1280

Solution

The correct option is 1280 because the function f(x) achieves its maximum and minimum values through the periodic behavior of the sine and cosine functions, leading to a specific range of outputs. By evaluating the function at critical points and using properties of trigonometric identities, we find that the difference M^4 - m^4 simplifies to 1280.

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