JEE Mains · Maths · STD 11 - Trigonometrical equations
If the sum of solutions of the system of equations \(2 \sin ^{2} \theta-\cos 2 \theta=0\) and \(2 \cos ^{2} \theta+3 \sin \theta=0\) in the interval \([0,2 \pi]\) is \(k \pi\), then \(k\) is equal to.
- A \(3\)
- B \(6\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(2 \sin ^{2} \theta-\cos 2 \theta=0\) \(2 \sin ^{2} \theta-\left(1-2 \sin ^{2} \theta\right)=0\) \(\sin ^{2} \theta=\left(\frac{1}{2}\right)^{2}\) \(\theta=\frac{\pi}{6}, \frac{5 \pi}{6}, \frac{7 \pi}{6}, \frac{11 \pi}{6}\) \(2 \cos ^{2} \theta+3 \sin \theta=0\)…
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