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Properties of Modulus

The number of...

Question

The number of solutions of $\sum_{r = 1}^{5} c o s r x = 5$ in the interval $[0, 2 π]$ is

A

0

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B

1

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C

5

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D

10

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Solution

The correct option is B
1

$∵ \sum_{r = 1}^{5} c o s r x = 5$

$\Rightarrow c o s x + c o s 2 x + c o s 3 x + c o s 4 x + c o s 5 x = 5$ which is possible only, when $c o s x = c o s 2 x = c o s 3 x = c o s 4 x = c o s 5 x$

= 1 and is satisfied by x = 0 only. Hence number of solution = 1.

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