Find the minimum value of the function $f (x) = (1 + sin x) (1 + cos x), \forall x ϵ R .$

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Solution

$f (x) = (1 + sin x) (1 + cos x), \forall x ϵ R .$
We know $| sin x |, | cos x | \leq 1$
Hence minimum value of $f (x)$ will occur when either $sin x, cos x = - 1$
Hence $f_{m i n} = 0$

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