AP EAMCET · Maths · Trigonometric Equations
If \(\sqrt{3} \cos \theta+\sin \theta>0\) then
- A \(-\frac{\pi}{2} < \theta < \frac{\pi}{2}\)
- B \(-\frac{\pi}{3} < \theta < \frac{2 \pi}{3}\)
- C \(-\frac{2 \pi}{3} < \theta < \frac{\pi}{3}\)
- D \(-\frac{\pi}{6} < \theta < \frac{5 \pi}{6}\)
Answer & Solution
Correct Answer
(B) \(-\frac{\pi}{3} < \theta < \frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(2 \left( \frac{\sqrt{3}}{2} \cos \theta + \frac{1}{2} \sin \theta \right) > 0\) \(2 \sin \left( \theta + \frac{\pi}{3} \right) > 0\) \(0 \(-\frac{\pi}{3} < \theta < \frac{2\pi}{3}\)
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