Thank you for reporting, we will resolve it shortly
Q.
$(sin \,\theta, cos \,\theta)$ and $(3, 2)$ lies on the same side of the line $x + y = 1$, then $\,\theta$ lies between
Straight Lines
Solution:
As $(sin\theta, cos\theta)$ and $(3, 2)$ lie on the same side of
$x + y - 1 = 0$, they should be of same sign.
$\therefore sin\theta + cos\theta - 1 > 0$ as $3 + 2 - 1 > 0$
$\Rightarrow \sqrt{2}sin\left(\theta+\frac{\pi}{4}\right) >1$
$\Rightarrow sin\left(\theta+\frac{\pi }{4}\right) > \frac{1}{\sqrt{2}} \Rightarrow 0 < \theta < \frac{\pi}{4}$