If $0 \leq x < 2 π$ , then the numbers of real values of $x$ , which satisfy the equation $cos x + cos 2 x + cos 3 x + cos 4 x = 0$ is:

7

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9

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3

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5

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Solution

The correct option is A $7$
cosx+cos2x+cos3x+cos4x=0

cos x + cos 3x + cos 2x + cos 6x = 0
2 cos 2x cos x + 2 cos 3x cos x = 0
2 cos x (cos 2x + cos 3x) = 0
4 cos x cos 5x/2 cos x/2 = 0
x = π/2, 3π/2, π/5, 3π/5, π, 7π/5, 9π/5
Total 7 values of x are possible.

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