The maximum value of $$fx=sin2x1+cos2xcos2x1+sin2xcos2xcos2xsin2xcos2xsin2x$$,x∈R is:

Question

The maximum value of $$fx=sin2x1+cos2xcos2x1+sin2xcos2xcos2xsin2xcos2xsin2x$$,x∈R is:

Infinity Learn · Accepted Answer

The given determinent $$fx=sin2x1+cos2xcox2x1+sin2xcos2xcox2xsin2xcos2xsin2x$$                                                $$=21+cos2xcox2x2cos2xcox2x1cos2xsin2x$$        $$C1$$→$$C1+C2$$                                                $$=0102cos2xcox2x1cos2xsin2x$$      $$R1$$→$$R1$$−$$R2Expand$$ the determinant                     $$fx=2sin2x$$−$$cos2xThe$$ maximum value of  $$acosx+bsinx$$ is $$a2+b2Hence$$ maximum  value of $$fx=22+1=5$$

$The maximum value of f (x) = |\begin{matrix} \sin^{2} x & 1 + \cos^{2} x & \cos 2 x \\ 1 + \sin^{2} x & \cos^{2} x & \cos 2 x \\ \sin^{2} x & \cos^{2} x & \sin 2 x \end{matrix}|, x \in R is:$

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The maximum value of fx=sin2x1+cos2xcos2x1+sin2xcos2xcos2xsin2xcos2xsin2x,x∈R is:

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$The maximum value of f (x) = |\begin{matrix} \sin^{2} x & 1 + \cos^{2} x & \cos 2 x \\ 1 + \sin^{2} x & \cos^{2} x & \cos 2 x \\ \sin^{2} x & \cos^{2} x & \sin 2 x \end{matrix}|, x \in R is:$