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Find the minimum value of (4^("Sin"^(2)x...

Find the minimum value of `(4^("Sin"^(2)x) + 4^("cos"^(2)x))` .

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Verified by Experts

Using A.M `ge` G.M. we have
`(4^("Sin"^(2)x) + 4^("cos"^(2)x))/(2) ge sqrt(4^("Sin"^(2)x), 4^("cos"^(2)x))`
`:. 4^("sin"^(2) x) + 4^("cos"^(2) x) ge 2 sqrt(4^("sin"^(2)x + "cos"^(2)x))`
`implies 4^("sin"^(2)x) + 4^("cos"^(2)x) ge 2 sqrt(4^(1))`
Hence, the minimum value of `4^("sin"^(2)x) + 4^("cos"^(2)x)` is 4.
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