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JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(sin\, 2x - 2\,cos\,x+ 4\,sin\, x\, = 4\) in the interval \([0, 5\pi ]\) is
- A \(3\)
- B \(5\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(\sin \,2x\, - 2\,\cos \,x\, + \,4\,\sin \,x\, = 4\) \( \Rightarrow \,2\,\sin \,x.\,\cos \,x - 2\,\cos \,x\, + \,4\,\sin \,x - 4 = 0\) \( \Rightarrow \,(\sin \,x - 1)(\cos \,x - 2)\, = \,0\) \(\because \,\cos \,x\, - \,2\, \ne \,0\,,\) \(\therefore \,\sin \,x\, = 1\)…
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