JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(0 \le x < 2\pi \) , then the number of real values of \(x,\) which satisfy the equation \(\cos x + \cos 2x + \cos 3x + \cos 4x = 0\) is . . .
- A \(7\)
- B \(9\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(7\)
Step-by-step Solution
Detailed explanation
\(\cos x+\cos 4 x+\cos 2 x+\cos 3 x=0\) \(\Rightarrow 2 \cos \left(\frac{5 x}{2}\right) \cos \left(\frac{3 x}{2}\right)+2 \cos \left(\frac{5 x}{2}\right) \cos \left(\frac{x}{2}\right)=0\) \(\Rightarrow 2 \cos \left(\frac{5 x}{2}\right) 2 \cos x \cos \left(\frac{x}{2}\right)=0\)…
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