Help showing equality involving $\tan$ function

Question

$$\Large\frac{\left(\frac{\tan \frac \pi 4+\tan x}{1-\tan\frac \pi 4\tan x}\right)}{\left(\frac{\tan \frac \pi 4-\tan x}{1+\tan\frac \pi 4\tan x}\right)}=\frac{\left(\frac{1+\tan x}{1-\tan x}\right)}{\left(\frac{1-\tan x}{1+\tan x}\right)}$$

I am having a little trouble figuring out how we got from the first step to the other one. It would be really appreciated if someone could help me out. Note that this is not an assignment question, these are all solved examples, only for my practice.

whats the value of $\tan(\frac{\pi}{4})$ ? – AgentS Aug 15 '14 at 14:16 — AgentS, Aug 15 '14 at 14:16
$\tan(\frac{\pi}{4})=?$ Draw the circle – Claude Leibovici Aug 15 '14 at 14:16 — Claude Leibovici, Aug 15 '14 at 14:16

score 3 · Accepted Answer · answered Aug 15 '14 at 14:16

3

Hint: $$\tan\frac\pi4=1\hspace{5mm} ;-){}{}{}{}$$

answered Aug 15 '14 at 14:16

MathGems

130

I feel soooooo stupid when doing trigonometry! :D Thanks. :) – Always Learning Forever Aug 15 '14 at 14:19
Feeling stupid is actually what makes us to move forward and remember things and importantly be better at things! :) – MathGems Aug 15 '14 at 14:21
Thank you so much for that. :) My exam is in one month and my math is a bit weak, so I'm kindda worried... – Always Learning Forever Aug 15 '14 at 14:24
Practice a lot, with time you will be way better and you'll pass your exam ;) Just keep practicing a lot – MathGems Aug 15 '14 at 14:25
@AkshatTripathi. Good luck for your exam ! – Claude Leibovici Aug 15 '14 at 14:43
@ClaudeLeibovici Thanks and I think that after a year of Stackoverflow, this is going to be my new best friend for this month! ;) :D – Always Learning Forever Aug 15 '14 at 14:44
@AkshatTripathi. This is a very, very, very good site ! I learn every single day and I bet I am older than your grand parents ! Cheers :-) – Claude Leibovici Aug 15 '14 at 14:46
@ClaudeLeibovici Wow! After so many years, still passionate about mathematics, I salute you, sir! :) – Always Learning Forever Aug 15 '14 at 14:50
@AkshatTripathi. Thank you ! I have a lot of fun with mathematics and I was very bad when young ! Work, work and discover the pure beauty ! – Claude Leibovici Aug 15 '14 at 14:52
@ClaudeLeibovici That was really motivating, thanks. :) – Always Learning Forever Aug 15 '14 at 14:53

score 1 · Answer 2 · answered Aug 15 '14 at 14:16

1

Hint:

$$\tan \frac{\pi}{4} = 1$$

answered Aug 15 '14 at 14:16

Darth Geek

12,296

Help showing equality involving $\tan$ function

2 Answers2