Question

The number of solutions of $\sum _{r=1}^4\cos rx=4$ in the interval $[0,2\pi ]$ is

• A. 1
• B. 0
• C. 4
• D. 3
• E. Infinite solutions

Answer 1

Answer: (A)

$\sum _{r=1}^4\cos rx=4$
$\cos x+\cos 2x+\cos 3x+\cos 4x=4$
Which is possible only iff,
$\cos x=\cos 2x=\cos 3x=\cos 4x=\cos 5x=1$
and it satisfied by $x=0$ only
$\therefore$ Number of solutions is $1$ .