trig question?

Question

prove identity
(1+Tanx)(Tan2x)= 2Tanx/1-Tanx
How is this possible? i tried everything! i have spent two hours trying to figure this one out but i cant!

Answer 1

Shouldn't you being your homework by urself? tiss tiss

Answer 2

Ok, so, to do this we must know the double angle formula for tangent:

tan(2x) = {(2tanx)/(1-tan^2(x)}

So, on the denominator we have a difference of the squares 1 and tan^2(x), so it can be factored to look like:

{(2tanx)/[(1 + tanx)(1 - tanx)]}

Now we plug that into the original formula:

(1 + tanx)*{2tanx/[(1 + tanx)(1 - tanx)]} = 2tanx/(1 - tanx)

On the left side, we cancel the (1 + tanx)'s out of the equation, to get:

2tanx/(1 - tanx) = 2tanx/(1 - tanx)

Thus the identity is proven.

Answer 3

use the formula tan 2x = 2tanx/(1-tan^2x)

(1+tanx) x 2tanx/(1-tan^2(x))
= (1+tanx) x 2 tanx /((1+tanx)(1-tanx))
=2 tanx /(1-tanx)
= rhs

Answer 4

tan 2x = 2 tan x / (1 - tan^2 x)

so
(1+tan x)(2 tan x/(1-tan^2 x))

(1+tan x)(2 tan x)
= ---------------------------
(1-tan^2 x)

(1+tan x) (2 tan x)
= -----------------------------
(1+ tan x) (1- tan x)

=2 tan x / 1 - tan x