Question

Evaluate $\frac{\cos {56}^{\circ }}{\sin {34}^{\circ }}$

Answer 1

The angles ${56}^{\circ }$ and ${34}^{\circ }$ are complementary. So, using trigonometric ratios of complementary angles $\cos {56}^{\circ }=\cos ({90}^{\circ }-{34}^{\circ })=\sin {34}^{\circ }$. Hence $\frac{\cos {56}^{\circ }}{\sin {34}^{\circ }}=\frac{\sin {34}^{\circ }}{\sin {34}^{\circ }}=1$