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

2 Answers
Nghi N. · Sunayan S · sjc · Nghi N
May 25, 2016

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

sjc
Nov 10, 2017

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

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