Correct Option: B

To solve this problem first calculate the fundamental period of the given signal i.e.,
x(t) = sin² t
or

x(t) =	1 – cos2x	= x(t) =	1 – cos2x
	2		2

(∴ cos² x = 1 – 2 sin² x)

∴ sin2x =	1 – cos2x
	2

FundamentaI period of x(t)

x(t) = T0 =	2π
	ω

=	2π	= π
	2

Now, x(t) = sin2t =		ejt – e–jf		2
		2j

= –	1	[e2jt – 2 + e– 2jt] ....…(A)
	4

Also given that Fourier series representation of x(t), i.e.,

	∞		∞
x(t) =		Ck ejkω0t =		Ck ejk2t …(B)
	– ∞		– ∞

In order to find the Fourier coefficients compare equation (A) and (B), we get

C1 = –	1
	4

C0 =	1
	2

C-1 = –	1
	4

and all other C_k = 0
Hence, alternative (B) is the correct choice.