[JEE Main 2016] the number of x in 0 2 pi satisfying cos x cos 2x cos
The number of $x\in[0,2\pi)$ satisfying $\cos x+\cos2x+\cos3x+\cos4x=0$ is
(a) $7$
(b) $9$
(c) $3$
(d) $5$
1 Answer
VAVidaara Admin
✓ Vidaara Team
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· 2d ago
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Correct answer: (a) $7$
Pairing gives $4\cos x\cos\frac{5x}2\cos\frac x2=0$. Distinct roots in $[0,2\pi)$: $\frac\pi5,\frac\pi2,\frac{3\pi}5,\pi,\frac{7\pi}5,\frac{3\pi}2,\frac{9\pi}5$ — seven.
JEE Main 2016 · Trigonometry — verified solution by the Vidaara Team.
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