Calculate the period of sin(x), tan(x), sin2(x) and tan2(x).

Please explain throughly.

as you know,

sin(kx) and cos(kx) have period 2pi/k
tan(kx) has period pi/k

sin^2(x) = (1-cos(2x))/2

use a similar trick to find the period of tan^2(x)

Looks like you need to review the basic info on trig functions.