Prove tan

[gary223]

Prove that tan(theta+45degrees) = 1+tantheta/1-tantheta

I got this so far:

tan(theta+45degrees) = tan theta + tan(45 degrees)/1-tan . tan(45 degrees)





Note:
May I suggest using LaTex on here, it would make the maths questions a lot more clearer. Just a tip.

[NickThissen]

I dunno how you got to your result, but I didn't come across that.

The only rules you need are:
tan x = sin x / cos x

sin(a + b) = sin a cos b + cos a sin b
cos(a + b) = cos a cos b - sin a sin b

And the value for sin(45 degrees) = sin(pi/4) and cos(45 degrees) = cos(pi/4).

You will get a result like
(A + B) / (C - D)
where A, B, C, D are sin or cos terms. Then it's a matter of rewriting that in terms of tan to get the final result.



I'd like LaTeX too but I don't think it's a trivial task. You'd have to have an interpreter/translator, an image generator and some place to store the images.

[jemidiah]

It seems like all you need is that cos(45 deg) = sin(45 deg), so tan(45 deg) = 1. This can be shown in many ways, probably most easily by drawing out a 45-45-90 triangle.