(TanX)-1)/(Tan(X)+1) = (1-cot(X))/(1+cot(X))

Question

Trig Identies

Answer 1

(TanX)-1)/(Tan(X)+1) = (1-cot(X))/(1+cot(X))

Let's make the "right side" of the equation look like the left:

(1-cot(X))/(1+cot(X))

since cot(x) = 1/tan(x) we can rewrite as:

(1-1/tan(x))/(1+1/tan(x))

(1-1/tan(x))/(1+1/tan(x)) * tan(x)/tan(x)

(tax(x)-1)/(tan(x)+1)  (which is exactly like the left side)