Prove that `(1 + tan x)/(1+cot x) = tan x`

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The identity `(1 + tan x)/(1 + cot x) = tan x` has to be proved.

`(1 + tan x)/(1 + cot x)`

=> `(1 + (sin x)/(cos x))/(1 + (cos x)/(sin x))`

=> `((cos x + sin x)/(cos x))/((sin x + cos x)/(sin x))`

=> `((cos x + sin x)/(sin x + cos x))*((sin x)/(cos x))`

=> `tan x`

This proves that `(1 + tan x)/(1 + cot x) = tan x`

jeew-m's profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

(1+tanx)/(1+cotx) = (1+tanx)/(1+1/tanx)

                            = ((1+tanx)/[(1+tanx)/tanx]

                            = (1+tanx)(tanx)/(1+tanx)

                            = tanx

We’ve answered 318,966 questions. We can answer yours, too.

Ask a question