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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 Im went wrong?