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Minimum value of 27^(cos 2x)*81^(sin 2x)...

Minimum value of `27^(cos 2x)*81^(sin 2x)` is

Text Solution

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Let
`y=27^(cos 2x)xx81(sin 2x)`
`=3^(3cos 2x)xx3^(4sin 2x)`
`=3^(3cos2x+4sin2x)`
Now, `-sqrt(3^(2)+4^(2))le3 cos 2x+4 sin 2xlesqrt(3^(2)+4^(2))`
`therefore -5le3cos 2x+4 sin 2xle5`
`rArr 3^(-5)le3^(3cos2x+4sin2x)le3^(5)`.
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