You are Here: Home >< A-levels

# Help with Maths Homework! Compound and Double angle formula !! watch

1. Find the value of tanx and hence solve the equation for 0<x<360
a) sin(x-30)=cosx
For this one I got x=30, 210 but I'm not sure if that's correct!
b) cos(x+60) = 2cos(x+30)
I am COMPLETELY stuck ...
Any help would be appreciated ! Thanks!
2. expand sin( x - 30° ) using sin ( A - B ) ≡ sinAcosB - cosAsinB
3. (Original post by the bear)
expand sin( x - 30° ) using sin ( A - B ) ≡ sinAcosB - cosAsinB
This.

And I'll also add that you should always just draw out sine and cosine curves if you're in any doubt. For example, if x was 30 in the first question (sin(x-30) = cos(x)) you'd get sin(0) = cos(30) which can't ever be true.
4. (Original post by the bear)
expand sin( x - 30° ) using sin ( A - B ) ≡ sinAcosB - cosAsinB
Which i've done and got : sin(x)cos(-30) - cos(x)sin(-30) = cosx Then I divided it by (cosx)(cos(-30)) Should I have done that?!
5. here A is x

B is 30° not -30°
6. (Original post by the bear)
here A is x

B is 30° not -30°

Ok so I've worked it out and I got: x=60,240

Part b)??
7. I wouldn't use addition formula unless you're specifically asked to here.
Note that . Then you get .
8. (Original post by Sophie_Banwell)
Ok so I've worked it out and I got: x=60,240

Part b)??
those look correct.

b) i would use the expansion for cos ( D + E )....
9. (Original post by the bear)
those look correct.

b) i would use the expansion for cos ( D + E )....

The cos(A+B)=cosAcosB+sinAsinB identity? So I would then get cosxcos60 + sinxsin60 = 2(cosxcos30 + sinxsin30) ??
10. (Original post by Sophie_Banwell)
The cos(A+B)=cosAcosB+sinAsinB identity? So I would then get cosxcos60 + sinxsin60 ??
there is a slight mistake in your version of the identity.
11. (Original post by the bear)
there is a slight mistake in your version of the identity.
Sorry a typo it should be : cos(A+B) = cosAcosB - sinAsinB So I would get: cosxcos60 - sinxsin60 = 2(cosxcos30 - sinxsin30) ??
12. (Original post by Sophie_Banwell)
Sorry a typo it should be : cos(A+B) = cosAcosB - sinAsinB So I would get: cosxcos60 - sinxsin60 = 2(cosxcos30 - sinxsin30) ??
yes
13. (Original post by the bear)
yes
Now what do I do? Do I divide it all by ((cosx)(cos30)) ?
14. (Original post by Sophie_Banwell)
Now what do I do? Do I divide it all by ((cosx)(cos30)) ?
you could divide each term by cosx ...
15. But if I divide by cos(x) I get :
tanx(2sin30-sin60) = 2cos30-cos60

Is this even right?
16. (Original post by the bear)
you could divide each term by cosx ...
But if I divide by cos(x) I get :
tanx(2sin30-sin60) = 2cos30-cos60

Is this even right?
17. (Original post by Sophie_Banwell)
But if I divide by cos(x) I get :
tanx(2sin30° -sin60° ) = 2cos30° -cos60°

Is this even right?
that looks fine...

now using your knowledge of special angles, replace the sin30° etc with fractions.

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: October 27, 2016
The home of Results and Clearing

### 2,563

people online now

### 1,567,000

students helped last year
Today on TSR

### GCSE results day guidance

All you need to know is here

### University open days

1. Bournemouth University
Wed, 22 Aug '18
2. University of Buckingham
Thu, 23 Aug '18
3. University of Glasgow
Tue, 28 Aug '18
Poll

## All the essentials

### Student life: what to expect

What it's really like going to uni

### Essay expert

Learn to write like a pro with our ultimate essay guide.

### Create a study plan

Get your head around what you need to do and when with the study planner tool.

### Resources by subject

Everything from mind maps to class notes.

### Study tips from A* students

Students who got top grades in their A-levels share their secrets