Project ForgeEngineering Mathematics
Calculus
GATE 2018
Medium
The Fourier cosine series for an even function f(x) is given by f(x) = a0 + Σ(n=1 to ∞) an cos(nx). The value of the coefficient a2 for the function f(x) = cos²(x) in [0, π] is
- A−0.5
- B0.0
- 0.5
- D1.0
Explanation
cos²(x) = (1+cos2x)/2 = 0.5 + 0.5cos(2x). Matching against a0 + Σan cos(nx), the coefficient of cos(2x) is a2 = 0.5.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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