Use the cosinus law to prove this formula

[Mewtwo]

Hey! I have a problem here that I can't solve, help would be greatly appreciated.

Homework Statement

In a triangle ABC with sides a, b and c, B is 60°. Use the cosinus law to prove this formula:

http://www4c.wolframalpha.com/Calculate/MSP/MSP54721a0508eiidf5ddbd00005aahbcg10134ag4h?MSPStoreType=image/gif&s=34&w=147&h=47

2. The attempt at a solution

I have no idea how to solve this so I was hoping you guys could at least point me in the right direction.

-Thanks in advance!

 

[micromass]

What does the cosine law state in this case?

 

[Mewtwo]

What does the cosine law state in this case?

Sorry, but what do you mean? I know the cosine law is: http://www4c.wolframalpha.com/Calculate/MSP/MSP45341a050abcb84ib7df000067dfbce6f994ai94?MSPStoreType=image/gif&s=10&w=167&h=18 but I just don't know what to do with it. Should I solve for c?

 

[micromass]

Sorry, but what do you mean? I know the cosine law is: http://www4c.wolframalpha.com/Calculate/MSP/MSP45341a050abcb84ib7df000067dfbce6f994ai94?MSPStoreType=image/gif&s=10&w=167&h=18 but I just don't know what to do with it. Should I solve for c?

Can you state the cosine law where you take cos(B) instead of cos(A)??

 

[Mewtwo]

Can you state the cosine law where you take cos(B) instead of cos(A)??

So I get http://www4c.wolframalpha.com/Calculate/MSP/MSP6381a050h93gegh83bh00001796145faf9g758g?MSPStoreType=image/gif&s=35&w=178&h=18 ? Sorry if I'm slow :/

 

[micromass]

And cos(60)=... ??

 

[Mewtwo]

And cos(60)=... ??

ok 0.5 so I get http://www4c.wolframalpha.com/Calculate/MSP/MSP11051a050h26b3g19eba000052d70cgif2ch1ich?MSPStoreType=image/gif&s=16&w=112&h=18 ?

 

[micromass]

Sorry, there was something wrong before that. If you switch A and B, then you also need to switch a, b and c around...

 

[Mewtwo]

Sorry, there was something wrong before that. If you switch A and B, then you also need to switch a, b and c around...

So I get http://www4c.wolframalpha.com/Calculate/MSP/MSP48411a050dgeddd2i67000003ecabg685d804cd1?MSPStoreType=image/gif&s=18&w=112&h=18 ?

 

[micromass]

Now try to work the formula in the OP into the formula you just found.

 

[Mewtwo]

Now try to work the formula in the OP into the formula you just found.

ok I got this http://www4c.wolframalpha.com/Calculate/MSP/MSP44471a050d98d94cbeec000020fe90ga7i8984hb?MSPStoreType=image/gif&s=9&w=210&h=54
Is that correct?