Evaluate:

$\dfrac{\text{cos 55°}}{\text{sin 35°}}$ + $\dfrac{\text{cot 35°}}{\text{tan 55°}}$

$\dfrac{\text{cos 55°}}{\text{sin 35°}} + \dfrac{\text{cot 35°}}{\text{tan 55°}}\\[1em] = \dfrac{\text{cos (90° - 45°)}}{\text{sin 35°}} + \dfrac{\text{cot (90° - 55°)}}{\text{tan 55°}}\\[1em] = \dfrac{\text{sin 45°}}{\text{sin 35°}} + \dfrac{\text{tan 55°}}{\text{tan 55°}}\\[1em] = \dfrac{\cancel{sin 45°}}{\cancel{sin 35°}} + \dfrac{\cancel{tan 55°}}{\cancel{tan 55°}}\\[1em] = 1 + 1\\[1em] = 2$

Hence, $\dfrac{\text{cos 55°}}{\text{sin 35°}} + \dfrac{\text{cot 35°}}{\text{tan 55°}}$ = 2.