**Signals And Systems By Palani**says that the fundamental period of sum, product of any signal is the LCM of their periods.

I have x(t) = sin(t) . cos(t) so the fundamental period of x(t) should be = LCM of 2pi and 2pi = 2pi

but as we know sin(t) . cos(t) = sin 2t and its period is pi (not 2pi) ??????

**Please help me with finding period of sum, difference, product, division, square, differentiation, integration e.t.c. of periodic signals**

Thanks in advance

Please help me it is highly needed