Let M and m respectively be the maximum and the minimum values of f ( x ) = 1 + sin 2 x sin 2 x sin 2 x cos 2 x 1 + cos 2 x cos 2 x 4 sin 4 x 4 sin 4 x 1 + 4 sin 4 x , x ∈ R Then M 4 − m 4 i

Question

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

TestHub · Accepted Answer

​ ​ 1 + sin 2 x sin 2 x sin 2 x ​ cos 2 x 1 + cos 2 x cos 2 x ​ 4 sin 4 x 4 sin 4 x 1 + 4 sin 4 x ​ ​ , x ∈ R R 2 ​ → R 2 ​ − R 1 ​ & R 3 ​ → R 3 ​ → R 1 ​ f ( x ) ​ 1 + sin 2 x − 1 − 1 ​ cos 2 x 1 0 ​ 4 sin 4 x 0 1 ​ ​ ​ Expand about R 1 ​ , use get f ( x ) = 2 + 4 sin 4 x ∴ M = max value of f ( x ) = 6 m = min value of f ( x ) = − 2 ∴ m 4 − M 4 = 1280

Mathematics - Determinant Question with Solution | TestHub

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