JEE Mains · Maths · STD 11 - 9. straight line
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 \(\left(0, \frac{\pi}{4}\right)\)
- B \(\left(0, \frac{3 \pi}{4}\right)\)
- C \(\left(\frac{\pi}{4}, \frac{3 \pi}{4}\right)\)
- D \(\left(0, \frac{\pi}{2}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(0, \frac{\pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given that both points (1,2)\(\&(\sin \theta, \cos \theta)\) lie on same side of the line \(x+y-1=0\) So, \((\) Put \((1,2)\) in given line \()(\operatorname{Put}(\sin \theta, \cos \theta)\) in given line\()>0\) \(\Rightarrow(1+2-1)(\sin \theta+\cos \theta-1)>0\)…
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