You are Here: Home >< Maths

# FP1 Help watch

1. Hey

I was given this problem in class while studying complex numbers but don't know where to start.

Prove that tan(pi/15) is a root of:
(t^4) - (6sqrt3)t^3 + 8(t^2) + (2sqrt3)t - 1 = 0

Any suggestions?

2. I haven't yet tried this, but my initial thought was the following. I don't know tan(pi/15), but I do know things like tan(pi/6), tan(pi/3), tan(pi/2). I also noticed that pi/3 was five times pi/15, i.e. tan(pi/3) = tan(5 * pi/15); moreover, initially I didn't have a clue where those sqrt(3) things were coming from, but now notice that tan(pi/3) = sqrt(3), and so tan(5 * pi/15) = sqrt(3).

So here's my idea, which I haven't checked, but I think will work: expand tan(5A) in terms of s = tan(A) (using complex numbers or whatever), and then put A = pi/15. Then just note that after rearrangement you show that s is a root of that equation you posted.
3. Update: it does work. You need to take out an "obvious"(!) factor from the resultant quintic. It's not too hard to spot.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 21, 2009
Today on TSR

### Edexcel C4 Maths Unofficial Markscheme

Find out how you've done here

### 1,880

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams