Expert: Steve Holleran - 8/3/2008

Question
help me. i cannot prove it.

show that the equation tan (45+x)=2tan (45-x)
can be written in the form
tan^2x-6tan x+1 = 0


Answer
Hi Ash,

Okay, I think this can be done using the formulas for tan(a + b) and  tan(a - b):

We have :                   tan(45 + x) = 2 * tan(45 - x)

[tan 45 + tan x]/[1-tan 45* tan x] = 2*[tan 45 - tan x/1+tan45 * tan x]

and, since tan 45 = 1, we have:

=[(1+tan x)/(1 - tan x)] = 2*[(1-tan x)/(1 + tan x)]

= [(1 + tan x)/(1 - tan x)] = [(2 - 2tan x)/(1 + tan x)]

Now cross-multiply:

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

 1 + 2tan x + tan^2 x           = 2 - 4 tan x + 2 tan^2 x

                   0 = tan^2 x - 6tan x + 1 = 0



Hope this helps, Steve