Trigonometric Identities

[phenolphthalein]

Hello, I need help with the following question.
Prove that the following equation is an identity.
tan x = sin (x + 2 pi ) / cos ( x - 2 pi )
I know that tan x = sin x / cos x ,but i don't know what to do with the 2 pi

 

[DrPhil]

Hello, I need help with the following question.
Prove that the following equation is an identity.
tan x = sin (x + 2 pi ) / cos ( x - 2 pi )
I know that tan x = sin x / cos x ,but i don't know what to do with the 2 pi

You should recognize (from having worked with the unit circle, perhaps) that all trig functions repeat with a period of 2pi. If you add n(2pi) to an angle, the result is the identical angle. You can use that argument to say sin(x+2pi) = sin(x), etc.

You could get to the same conclusion using sin(A±B) and cos(A±B) formulas, with A=x and B=2pi.