Expert Answers

An illustration of the letter 'A' in a speech bubbles

You should use the following formula to prove that expression `tan(pi+x) = tan x`  holds, such that:

`tan(a+b) = (tan a+tan b)/(1 - tan a*tan b)`

Reasoning by analogy yields:

`tan(pi+x) = (tan pi+tan x)/(1 - tan pi*tan x)`

Substituting 0 for `tan pi`  yields:

`tan(pi+x) = (0+tan x)/(1 -...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

You should use the following formula to prove that expression `tan(pi+x) = tan x`  holds, such that:

`tan(a+b) = (tan a+tan b)/(1 - tan a*tan b)`

Reasoning by analogy yields:

`tan(pi+x) = (tan pi+tan x)/(1 - tan pi*tan x)`

Substituting 0 for `tan pi`  yields:

`tan(pi+x) = (0+tan x)/(1 - 0*tan x)`

`tan(pi+x) = (tan x)/1 => tan(pi+x) = tan x`

Hence, using the formula `tan(a+b) = (tan a+tan b)/(1 - tan a*tan b)`  to evaluate the given expression yields that `tan(pi+x) = tan x`  is valid.

Approved by eNotes Editorial Team