Q.Using the complementary-angle relation, evaluate: $\dfrac{\cos80°}{\sin10°}$.

Since $80°$ and $10°$ are complementary, $\cos80°$ can be rewritten as $\sin10°$, which cancels directly against the denominator.

Step 1 — notice that $80°$ and $10°$ are complementary (they add to $90°$), and write $80°=90°-10°$.

Step 2 — apply the complementary-angle relation.

$\cos80° = \cos(90°-10°) = \sin10°$ …

Trying to evaluate $\cos80°$ and $\sin10°$ as separate decimal approximations misses the point of the complementary relation entirely, and is also outside this chapter's exact-value scop …