Sine of Complement equals Cosine/Proof 4

Proof

 * ComplementaryAngles.png

Let $\angle xOP$ and $\angle QOy$ be complementary.

Then:
 * $\angle xOP = \angle QOy$

Hence:
 * the projection of $OP$ on the $x$-axis

equals:
 * the projection of $OQ$ on the $y$-axis.

Hence the result.