A periodic signal x(t) has a trigonometric Fourier series expansion $$x\left( t \right) = {a_0} + \sum\limits_{n = 1}^\infty {\left( {{a_n}\cos n{\omega _0}t + {b_n}\sin n{\omega _0}t} \right)} $$
If $$x\left( t \right) = - x\left( { - t} \right) = - x\left( {t - \frac{\pi }{{{\omega _0}}}} \right),$$      we can conclude that

A. a_n are zero for all n and b_n are zero for n even

B. a_n are zero for all n and b_n are zero for n odd

C. a_n are zero for n even and b_n are zero for n odd

D. a_n are zero for n odd and b_n are zero for n even

Answer: Option A