AP EAMCET · Maths · Straight Lines
If \(P(\sin \alpha, \cos \alpha)\) lies inside the triangle formed by the vertices \((0,0),\left(\sqrt{\frac{3}{2}}, 0\right)\) and \(\left(0, \sqrt{\frac{3}{2}}\right)\), then \(\alpha\) lies in the interval
- A \(\left(0, \frac{\pi}{3}\right)\)
- B \(\left(0, \frac{\pi}{4}\right)\)
- C \(\left(0, \frac{\pi}{6}\right)\)
- D \(\left(0, \frac{\pi}{12}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(0, \frac{\pi}{12}\right)\)
Step-by-step Solution
Detailed explanation
\(P\) and \(A\) will lie on the same side of \(x=0\). \(\therefore \quad \sin \alpha>0\) ...(i) \(P\) and \(\dot{B}\) will lie on the same side of \(y=0\). \(\therefore \quad \cos \alpha>0\) ...(ii) \(P\) and \(O\) will lie on the same side of \(x+y=\sqrt{\frac{3}{2}}\).…
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