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

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justaguide eNotes educator| Certified Educator

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 eNotes educator| Certified Educator

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

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

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

                            = tanx