Let f (x) = left| {begin{array}{*{20}{c}}{1, + ,{{sin }^2}x}&{{{cos }^2}x}&{4,sin ,2x}{{{sin

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3 and 4 .Determinants and Matrices

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Let $f (x) =$ $\left| {\begin{array}{*{20}{c}}{1\, + \,{{\sin }^2}x}&{{{\cos }^2}x}&{4\,\sin \,2x}\\{{{\sin }^2}x}&{1\, + \,{{\cos }^2}x}&{4\,\sin \,2x}\\{{{\sin }^2}x}&{{{\cos }^2}x}&{1\, + \,4\,\sin \,2x}\end{array}} \right|$, then the maximum value of $f (x) =$

A

$2$

B

$4$

C

$6$

D

$8$

Solution

Use $R_1 \rightarrow R_1 – R_2 \, \& \, R_2 \rightarrow R_2 – R_3$ and expand to get $f(x) = 2 + 4 \, \sin \, 2x$

Standard 12

Mathematics

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