TIFR ECE 2014 | Question: 6

Question

Let $g:[0, \pi] \rightarrow \mathbb{R}$ be continuous and satisfy
\[
\int_{0}^{\pi} g(x) \sin (n x) d x=0
\]
for all integers $n \geq 2$. Then which of the following can you say about $g?$ 

• A. $g$ must be identically zero.
• B. $g(\pi / 2)=1$.
• C. $g$ need not be identically zero.
• D. $g(\pi)=0$.
• E. None of the above.