If $0 \leq x < 2 π$ , then the number of real values of x, which satisfy the equation cosx + cos2x + cos3x + cos4x = 0, is:

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Solution

The correct option is B
7

$c o s x + c o s 2 x + c o s 3 x + c o s 4 x = 0 2 c o s \frac{5 x}{2} . c o s \frac{3 x}{2} + 2 c o s \frac{5 x}{2} . c o s \frac{x}{2} = 0 2 c o s \frac{5 x}{2} \times 2 c o s x \times c o s \frac{x}{2} = 0 x = \frac{(2 n + 1) π}{5}, \frac{(2 k + 1) π}{2}, (2 r + 1) π W h e r e n, k, ϵ Z 0 \leq x < 2 π H e n c e x = \frac{π}{5}, \frac{3 π}{5}, π, \frac{2 π}{5}, \frac{9 π}{5}, \frac{π}{2}, \frac{3 π}{2}$

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