The number of solutions of ∑5r=1cos r x=5 in the interval [0,2π] is
1
∵∑5r=1cos r x=5
⇒cos x+cos 2x+cos 3x+cos 4x+cos 5x=5 which is possible only, when cos x=cos 2x=cos 3x=cos 4x=cos 5x
= 1 and is satisfied by x = 0 only. Hence number of solution = 1.