Find the period of the following function

[chaoseverlasting]

I was asked to find the period of the following function:

f(x)= mod(sinx)/cosx + mod(cosx)/sinx

Since modulus is defined as sqrt(x*x),

mod(sinx)/cosx= (sqrt(1-cosx*cosx))/ cosx
= sqrt(1/cosx*cosx -1) //Taking cosx into the square root
= sqrt(secx*secx-1)
= sqrt(tanx)
= mod(tanx)

and similarly, mod(cosx)/sinx = mod(cotx)
which is not possible because if either cosx or sinx are negative, then mod(cotx) or mod(tanx) will be negative.

Could someone point our where I am went wrong?

 

[arildno]

1. cos(x)=sign(cos(x))*|cos(x)|
2. sec(x)*sec(x)-1 equals tan(x) SQUARED.