Evaluate:

$\dfrac{\text{sec 75°}}{\text{cosec 15°}}$

$\dfrac{\text{sec 75°}}{\text{cosec 15°}} = \dfrac{\text{sec (90° - 15°)}}{\text{cosec 15°}}\\[1em] = \dfrac{\text{cosec 15°}}{\text{cosec 15°}}\\[1em] = \dfrac{\cancel{cosec 15°}}{\cancel{cosec 15°}}\\[1em] = 1$

Hence, $\dfrac{\text{sec 75°}}{\text{cosec 15°}}$ = 1.