Let A=5sin2θcos2θ−sin2θ−51cos2θ15⋅ Then maximum value of A=

A=−130+5sin4θ+5cos4θ =−130+51−12sin22θMax value ofA is for min value of sin22θ∴ Max value of A =-125

Let A=5sin2θcos2θ−sin2θ−51cos2θ15⋅ Then maximum value of A=

A=−130+5sin4θ+5cos4θ =−130+51−12sin22θMax value ofA is for min value of sin22θ∴ Max value of A =-125

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Let $A = [\begin{matrix} 5 & \sin^{2} θ & \cos^{2} θ \\ - \sin^{2} θ & - 5 & 1 \\ \cos^{2} θ & 1 & 5 \end{matrix}] \cdot$ Then maximum value of $|A| =$

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-125

200

$\frac{- 255}{2}$

145

answer is A.

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Detailed Solution

$|A| = - 130 + 5 \sin^{4} θ + 5 \cos^{4} θ$
$= - 130 + 5 [1 - \frac{1}{2} \sin^{2} 2 θ]$
Max value of $|A|$ is for min value of $\sin^{2} 2 θ$
$∴$ Max value of $|A|$ =-125

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Let A=5sin2θcos2θ−sin2θ−51cos2θ15⋅ Then maximum value of A=

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Let $A = [\begin{matrix} 5 & \sin^{2} θ & \cos^{2} θ \\ - \sin^{2} θ & - 5 & 1 \\ \cos^{2} θ & 1 & 5 \end{matrix}] \cdot$ Then maximum value of $|A| =$