Verifying the identity (sin x + tan x)/(1 + cos x) = tan x

[dec1ble]

im trying to verify this identity - sin x + tan x / 1 + cos x = tan x - i get lost very easily and need the steps - can anyone help me?

 

[Tide]

It might help if you took a little more care in writing your expressions with suitable placement of parentheses and properly distinguishing between hyphens and minus signs.

 

[HallsofIvy]

Tide's point is that it is not clear if you mean (sin x+ tan x)/(1+ cos x) or
sin x+ (tan x/(1+ cos x), or (-sin x+ tan x)/(1+ cos x) or...

Probably you mean (sin x+ tan x)/(1+ cos x)= tan x.

Hint: replace tan x by sin x/cos x. Then do the algebra to simplify the left side.
(1+ cos x is important!)