Q.Simplify: $\sin(90°-\theta)\cdot\sec\theta$.

The complementary-angle relation rewrites $\sin(90°-\theta)$ as a cosine, which then cancels against the secant.

Step 1 — apply the complementary-angle relation.

Step 2 — substitute.

$\sin(90°-\theta)\cdot\sec\theta = \cos\theta\cdot\sec\theta$ …

Confusing the complementary relation with the reciprocal relation is a frequent slip — $\sin(90°-\theta)$ equals $\cos\theta$ (a DIFFERENT ratio of the SAME angle's complem …