Explanation

(a)
Given points $(\sin\theta,\cos\theta)$ and (3, 2) and a line
$x + y - 1 = 0$ ..(i)
Since, (3,2) lies on Eq. (i)
$3 + 2 - 1 > 0$
And $(\sin\theta,\cos\theta)$ lies in Eq. (i)
$\therefore\sin\theta + \cos\theta - 1 > 0$
$\Rightarrow \ \sin\theta + \cos\theta > 1$
$\Rightarrow \ \sqrt{2}\left\lbrack \sin\left( \theta + \frac{\pi}{4} \right) \right\rbrack > 1$
$\Rightarrow \ \sin\left( \theta + \frac{\pi}{4} \right) > \frac{1}{\sqrt{2}} = \sin\left( \frac{\pi}{4} \right)$
$\Rightarrow \ 0 < \theta < \frac{\pi}{2}$