\(\sec\theta = \csc\phi\) Or, \(\sec\theta = \sec(90^\circ - \phi)\) So, \(\theta = 90^\circ - \phi\) Therefore, \(\theta + \phi = 90^\circ\) \(\therefore \csc(\theta + \phi) = \csc 90^\circ = 1\) (Answer)
\(\sec\theta = \csc\phi\) Or, \(\sec\theta = \sec(90^\circ - \phi)\) So, \(\theta = 90^\circ - \phi\) Therefore, \(\theta + \phi = 90^\circ\) \(\therefore \csc(\theta + \phi) = \csc 90^\circ = 1\) (Answer)