Question

1 over 1+tanx + 1 over 1+cotx =1

Answer 1

Verify the identities

Answer 2

is it
\[\frac{1}{1+\tan(x)}+\frac{1}{1+\cot(x)}=1\]?

Answer 3

Set tan(x) = a/b and cot(x) = b/a. Simplify. Result follows.

Answer 4

Yea @satellite73

Answer 5

@Gabysolis49
cot = 1/tan
\[\frac{1}{1+\tan x}+\frac{1}{1+\frac{1}{\tan x}}\]
\[=\frac{1}{1+\tan x}+\frac{1}{\frac{\tan x}{\tan x}+\frac{1}{\tan x}}\]
\[=\frac{1}{1+\tan x}+\frac{1}{\frac{\tan x +1}{\tan x}}\]
\[=\frac{1}{1+\tan x}+\frac{\tan x}{1+\tan x}\]
\[=\frac{1+\tan x}{1+\tan x}\]
\[=1\]