How do you prove (tan(x)-1)/(tan(x)+1)= (1-cot(x))/(1+cot(x))?

2 Answers
Apr 19, 2015

Start off by cross multiplying

(tanx-1)(1+cotx)=(tanx+1)(1-cotx)

Expand each side using FOIL

tanx+tanxcotx-1-cotx
=tanx-tanxcotx+1-cotx

Since tanx and cotx are reciprocals

tanxcotx=1

Now we can write

tanx+1-1-cotx=tanx-1+1-cotx

Simplifying each side

tanx-cotx=tanx-cotx

The right hand side and left hand side are the same