The Fourier series for f(x) = sin2 x defined over the range -π ≤ x ≤ π is

This question was previously asked in
UPSC IES Electrical 2022 Prelims Official Paper
View all UPSC IES Papers >
  1. \(\frac{1}{2}-\frac{\cos 2x}{2}\)
  2. 1 + cos 2x
  3. \(\frac{1}{2}-\frac{\cos x}{2}\)
  4. \(\frac{\cos 2x}{2}+\frac{1}{2}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{1}{2}-\frac{\cos 2x}{2}\)
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
6.2 K Users
20 Questions 40 Marks 24 Mins

Detailed Solution

Download Solution PDF

Calculation:

From the trigonometric identity:

cos (2x) = 1 - 2sin2(x)

2sin2(x) = 1 - cos (2x)

f(x) = sin2 x = \(\frac{1}{2}-\frac{\cos 2x}{2}\)

Hence, option 1 is correct.

Latest UPSC IES Updates

Last updated on May 28, 2025

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

More Calculus Questions

Get Free Access Now
Hot Links: teen patti star apk teen patti gold old version teen patti master 2025