JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(S\, = \,\left\{ {\theta \, \in \,[ - \,2\,\pi ,\,\,2\,\pi ]\, :\,2\,{{\cos }^2}\,\theta \, + \,3\,\sin \,\theta \, = \,0} \right\}\). Then the sum of the elements of \(S\) is
- A \(\frac{{13\,\pi }}{6}\)
- B \(2\pi \)
- C \(\pi \)
- D \(\frac{{5\,\pi }}{3}\)
Answer & Solution
Correct Answer
(B) \(2\pi \)
Step-by-step Solution
Detailed explanation
\(2\,(1 - {\sin ^2}\theta )\, + \,3\,\sin \,\theta \, = \,0\) \( \Rightarrow {\kern 1pt} 2\,{\sin ^2}\theta \, - \,3\sin \,\theta \, - \,2\, = \,0\) \( \Rightarrow (2\,\sin \theta + 1)(\sin \theta - 2) = 0\)…
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