Evaluate :
$sin (90^{o} - A) sin A - cos (90^{o} - A) cos A$

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Solution

Use the formula:
$s i n (90^{\circ} - A) = c o s A$ and $c o s (90^{\circ} - A) = s i n A$

So,
$s i n (90^{\circ} - A) s i n A - c o s (90^{\circ} - A) c o s A$
$= c o s A s i n A - s i n A c o s A$
$= 0$

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