Question

How do you simplify `(1+tan(x)) / (1+cot(x))`?

Answer 1

The answer is : `tan x`

Explanation:

`(1 + tan x)/(1 + cot x)`
`= (1 + tan x)/(1 + 1/(tan x)`
`= (1 + tan x)/(tan x + 1)cdottan x`
`=cancelcolor(red)(1 + tan x)/cancelcolor(red)(tan x + 1)cdottan x`
`=tanx`

Answer 2

`tanx`

Explanation:

if you're not sure how to start then change everything to sine and cosines

`(1+tanx)/(1+cotx)=(1+(sinx/cosx))/(1+(cosx/sinx))`

`=((cosx+sinx)/cosx)/((sinx+cosx)/sinx)`

`=(1/cosx)/(1/sinx)=sinx/cosx=tanx`