JEE Mains · Maths · STD 11 - Trigonometrical equations
The sum of all values of \(\theta \in[0,2 \pi]\) satisfying \(2 \sin ^2 \theta=\cos 2 \theta\) and \(2 \cos ^2 \theta=3 \sin \theta\) is
- A \(4 \pi\)
- B \(\frac{5 \pi}{6}\)
- C \(\pi\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\pi\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 2 \sin ^2 \theta=\cos 2 \theta \\ & 2 \sin ^2 \theta=1-2 \sin ^2 \theta \\ & 4 \sin ^2 \theta=1 \\ & \sin ^2 \theta=\frac{1}{4} \\ & \sin \theta= \pm \frac{1}{2} \\ & 2 \cos ^2 \theta=3 \sin \theta \\ & 2-2 \sin ^2 \theta+3 \sin \theta-2=0 \\ & (2 \sin…
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