JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(4 \sin ^2 x-4\) \(\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]\) is :
- A \(1\)
- B \(3\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
\( 4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi] \) \( 4-4 \cos ^2 x-4 \cos ^3 x+9-4 \cos x=0 \) \( 4 \cos ^3 x+4 \cos ^2 x+4 \cos x-13=0 \) \( 4 \cos ^3 x+4 \cos ^2 x+4 \cos x=13 \) \( \text { L.H.S. } \leq 12 \text { can't be equal to } 13 .\)
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