Trigonometrical Equations 1 Question 10

10. If $0 \leq x<2 \pi$, then the number of real values of $x$, which satisfy the equation

$\cos x+\cos 2 x+\cos 3 x+\cos 4 x=0$, is (2016 Main)

(a) 3

(b) 5

(c) 7

(d) 9

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Answer:

Correct Answer: 10. (c)

Solution:

  1. Given equation is $\cos x+\cos 2 x+\cos 3 x+\cos 4 x=0$

$\Rightarrow \quad(\cos x+\cos 3 x)+(\cos 2 x+\cos 4 x)=0$



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