JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(|\cot x|=\cot x+\frac{1}{\sin x}\) in the interval \([0,2 \pi]\) is
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
If \(\cot x>0 \Rightarrow \frac{1}{\sin x}=0\) (Not possible) If \(\operatorname{cotx}<0 \Rightarrow 2 \cot x+\frac{1}{\sin x}=0\) \(\Rightarrow 2 \cos x=-1\) \(\Rightarrow x =\frac{2 \pi}{3}\) or \(\frac{4 \pi}{3}( reject )\)
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