Question

The set of all possible values of $\theta$ in the interval $(0,\pi )$ for which the points $(1,2)$ and $(\sin \theta ,\cos \theta )$ lie on the same side of the line $x+y=1$ is:

• A. $(0,\frac{\pi }{4})$
• B. $(0,\frac{\pi }{2})$
• C. $(0,\frac{3\pi }{4})$
• D. $(\frac{\pi }{4},\frac{3\pi }{4})$

Answer 1

The correct option is B $(0,\frac{\pi }{2})$


$L_{11}\times L_{22}>0$
$\Rightarrow \sin \theta +\cos \theta >1$
$\Rightarrow \theta \in (0,\frac{\pi }{2})$