How do you prove (1+tan x) / (1+cot x) = 2?
1 Answer
Feb 19, 2016
It is not an identity and thus, it can't be proven.
Explanation:
You can't prove it since it's not an identity.
Let's transform the left side using
tan x = sin x / cos x ," " cot x = cos x / sin x
We have
(1 + tan x ) / (1 + cot x ) = (1 + sin x / cos x) / (1 + cos x / sin x)
= (cos x/ cos x + sin x / cos x) / (sin x / sin x + cos x / sin x)
= ( (cos x + sin x) / cos x) / ( (sin x + cos x) / sin x)
= (cos x + sin x) / cos x * sin x / (sin x + cos x)
= (cancel((cos x + sin x)) * sin x) / (cos x * (cancel(sin x + cos x)))
= sin x / cos x
= tan x
However,
Thus, your equation is not an identity and can't be proven.