Find the maximum & minimum values of $27^{cos 2 x} 81^{sin 2 x}$

Minimum Value

= 3^{- 5}

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Minimum Value

= 3^{- 4}

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Minimum Value

= 3^{- 3}

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Minimum Value

= 3^{- 6}

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Solution

The correct option is B Minimum Value $= 3^{- 5}$
The value of $27^{cos 2 x} 81^{sin 2 x}$

$= 3^{3 cos 2 x} 3^{4 sin 2 x} = 3^{(3 sin 2 x + 4 cos 2 x)}$

$\Rightarrow$ As $- 5 \leq 3 sin 2 x + 4 cos 2 x \leq 5$

$∴ 3^{- 5} \leq 27^{cos 2 x} 81^{sin 2 x} \leq 3^{5}$

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