Show that `sin theta and cos theta` are periodic functions.

Why sin theta , cos theta are periodic functions?

The trigonometric functions tan theta, cot theta are periodic but not simple harmonic, whereas sin theta and cos theta are periodic as well as simple harmonic. Why ?

If 5 tan theta = 4 , show that ( 5 sin theta - 3 cos theta)/(5 sin theta + 3 cos theta) = (1)/(7)

cos theta+sin theta=cos2 theta+sin2 theta

If tan theta=(a)/(b), show that (a sin theta-b cos theta)/(a sin theta+b cos theta)=(a^(2)-b^(2))/(a^(2)+b^(2))

If 3 cot theta= 2 , show that ((4 sin theta - 3 cos theta ))/((2 sin theta + 6 cos theta))=(1)/(3)

If sin theta+cos theta=1, then sin theta cos theta is equal to :

If 3 tan theta =4, show that ((4 cos theta -sin theta))/((a cos theta + sin theta ))=7/25

Show that equations x=a cos theta + b sin theta, y = a sin theta - b cos theta represents a circle, wheter theta is a parameter.