Explanation

(c)
Given that$,\sin{\theta + \cos{\theta = m\ \ \ldots(i)}}$
and$\ \sec{\theta + cosec\ \theta = n\ \ \ \ \ \ \ \ \ \ \ \ldots(ii)}$
Now,$\ n(m + 1)(m - 1) = n(m^{2} - 1)$
$= (\sec{\theta + cosec\ \theta)2\sin{\theta\cos\theta}}$ ${(\because m}^{2} = 1 + 2\sin{\theta\cos{\theta)}}$
$= \frac{\sin{\theta + \cos\theta}}{\sin{\theta\cos\theta}}2\sin{\theta\cos\theta}$
$= 2m\ \ \ \ \ \$[from Eq.(i)]