Given f (x) = cos[π2]x+cos[−π2x] As π = 3.141 ⇒ π2 = 9.8 (approx) Using definition of greatest integer function [π2] = [9.8] = 9 and [−π2] = [- 9.8] = - 10 ∴ f (x) = cos 9x + cos (- 10) x = cos 9x + cos 10x [Since cos (- θ) = cos θ] f(
π
4
) = cos
9π
4
+cos
10π
4
= cos (2π+
π
4
) + cos (2π+
2π
4
) = cos
π
4
+ cos
π
2
=
1
√2
+0 =
1
√2
Similarly, f (- π) = cos (- π) + cos (- 10π) = cos 9π + cos 10π = - 1 + 1 = 0 Also f (π) = cos -π + cos 10π = - 1 + 1 = 0 f(