AP EAMCET · Maths · Trigonometric Equations
The number of solutions of the equation \(2 \sin ^2 \theta-3 \cos ^2 \theta=\sin \theta \cos \theta\) lying in the interval \((-\pi, \pi)\) is
- A \(2\)
- B \(4\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(2 \tan ^2 \theta - 3 = \tan \theta\) \(2 \tan ^2 \theta - \tan \theta - 3 = 0\) \((2 \tan \theta - 3)(\tan \theta + 1) = 0\) \(\tan \theta = 3/2\) or \(\tan \theta = -1\) If \(\tan \theta = 3/2\), let \(\alpha = \arctan(3/2)\). Solutions in \((-\pi, \pi)\) are…
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