#### Answer

0

#### Work Step by Step

$f(a+\Delta x)-f(a)\approx f'(a)\Delta x$
$\implies \sin (\frac{\pi}{2}+0.1)-\sin \frac{\pi}{2}=\frac{d}{dx} (\sin x) |_{x=\frac{\pi}{2}}\times0.1$
$=\cos \frac{\pi}{2}\times0.1= 0\times0.1=0$

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