Explanation

(b)
Given, $cosec\ \theta - \sec{\theta = cosec\ \theta.\sec\theta}$
$\Rightarrow \ \frac{\cos{\theta - \sin\theta}}{\cos{\theta\sin\theta}} = \frac{1}{\cos{\theta\sin\theta}}$
$\Rightarrow \ \ \cos{\theta - \sin{\theta = 1\ \ \ \Rightarrow \ \ \ \cos\left( \frac{\pi}{4} + \theta \right) = \frac{1}{\sqrt{2}}}}$
$\Rightarrow \ \frac{\pi}{4} + \theta = 2n\pi \pm \frac{\pi}{4}\ \ \ \ \Rightarrow$ Solution exist
$cosec\ \theta.\sec{\theta = 1}$
$\Rightarrow \ \sin{\theta\cos{\theta = 1}}$
$\Rightarrow \ 2\sin{\theta\cos{\theta = 2}}$
$\Rightarrow \ \sin{2\theta =}2$
As we know $\sin\theta$ is not greater than 1
$\therefore$ The above equation has no solution exist