You are Here: Home >< Maths

# proving a trig equation watch

1. Hello,
Does anyone know how to prove that

?

I'm getting extremely confused!!

(Also obviously having trouble using symbols!)
2. That's not true. Maybe it should read:

Do you know the formulae for and ?
3. apologies, that is what it is suppposed to read. no, i dont think i do. or, i did know and i have now forgotten? either are very possible!!
4. (Original post by kate__88)
apologies, that is what it is suppposed to read. no, i dont think i do. or, i did know and i have now forgotten? either are very possible!!
Well I'll tell you the identities you can use. See if you can do it now.

5. i'm thinking that the second identity fits this equation better. but there are differing values for A and b...
6. or do you use both??
7. Yeah use both.
8. haha oh dear still not getting anywhere. which values do you use for a and b? are the values you use different for the two different equations. i'm never any good at proving things!!
9. I'm gonna let theta = x here

cos(pi/3 -x) + sin(pi/6 - x)

Using cos(A-B) = cos(A)cos(B) + sin(A)sin(B)
cos(pi/3 - x) = cos(pi/3)cos(x) + sin(pi/3)sin(x) (here A = pi/3 and B =x)

Using sin(A-B) = sin(A)cos(B) - sin(B)cos(A)
sin(pi/6 - x) = sin(pi/6)cos(x) - sin(x)cos(pi/6)

Therefore:

cos(pi/3 -x) + sin(pi/6 - x)
= cos(pi/3)cos(x) + sin(pi/3)sin(x) + sin(pi/6)cos(x) - sin(x)cos(pi/6)

Try it from there?

You have to realise that equations like sin(A-B) = sin(A)cos(B) - sin(B)cos(A) are actually identities - they're true for all values of A and B. It's not like simultaneous equations that you need to have two equations with the same A and B.
10. i got to the two separate equations before (with the help of the suggestion of the identities) by assuming that A and B would be different. i did the same steps, but i was unable to merge the equations. i understand how you have merged the two equations but unfortunately i'm still struggling to come to the final line where cos theta will equal that equation??? any other hints please? (without of course completely giving me the answer! )
11. Notice how cos(pi/3) is a number. Maybe it will help to actually write down what cos(pi/3), sin(pi/6) etc actually are?
12. yaya!! i got it! thanks so much for all your help!!

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: August 26, 2007
Today on TSR

### TSR Pub Quiz 2018 - Anime

The first of our week-long series of entertainment quizzes

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '18
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