Answer
$ 1$
Work Step by Step
Use the definition and properties of trig functions, we have:
$sec52^\circ cos308^\circ=\frac{cos308^\circ}{cos52^\circ} =\frac{cos(360-52)^\circ}{cos52^\circ}=\frac{cos(52)^\circ}{cos52^\circ}=1$
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