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anonymous

  • 5 years ago

Can someone help me to prove this? (cosA+cosB)/(cosA-cosB)=cot((1/2)(A-B))cot((1/2)(A+B))

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  1. anonymous
    • 5 years ago
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    we can use a few identities to rewrite the right hand side. First right it as product of two cosines over product of two sines. Then I used cos(u +/- v)= cos(u)cos(v) -/+ sin(u)sin(v) sin(u +/- v)= sin(u)cos(v) +/- cos(u)sin(v) sin^2(x)=(1-cos(2x))/2 cos^2(x)=(1+cos(2x))/2. its just a matter of running the algebra then. Let me know if you need help with any steps or getting started.

  2. anonymous
    • 5 years ago
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    write*

  3. anonymous
    • 5 years ago
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    yeah I need help. Im really confused with this

  4. anonymous
    • 5 years ago
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    Please can you show me the work?

  5. anonymous
    • 5 years ago
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    Trying to learn trigonometry

  6. anonymous
    • 5 years ago
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    ok the right hand side can be written... {cos((A-B)/2)*cos((A+B)/2)}/{sin((A-B)/2)*sin((A+B)/2)}

  7. anonymous
    • 5 years ago
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    each term is in the form of the first 2 identities that i posted

  8. anonymous
    • 5 years ago
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    so if you write them out and then multiply you'll get terms in the form of the 3rd and 4th identities I posted

  9. anonymous
    • 5 years ago
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    It all simplifies down to the left hand side

  10. anonymous
    • 5 years ago
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    let me check it out. I will write you if i get lost. Thanks

  11. anonymous
    • 5 years ago
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    Yep let me know.

  12. anonymous
    • 5 years ago
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    http://www.sosmath.com/trig/Trig5/trig5/trig5.html here are a bunch of identities

  13. anonymous
    • 5 years ago
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    These trig problems are always mindless manipulation of symbols. I'll have a go at it and get back to you shortly.

  14. anonymous
    • 5 years ago
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    got it!

  15. anonymous
    • 5 years ago
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    good :)

  16. anonymous
    • 5 years ago
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    OK. The sum and difference formulae for cosines are as follows: CosA + CosB = 2cos((A+B)/2)cos((A-B)/2) and CosA - CosB = -2sin((A+B)/2)sin((a-B)/2) So, your LHS = -cot((A+B)/2)cot((A-B)/2) Note. I have a minus sign in front of your solution.

  17. anonymous
    • 5 years ago
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    i had a negative as well

  18. anonymous
    • 5 years ago
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    yeah the solution has a - sign

  19. anonymous
    • 5 years ago
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    emun i answered one of your old physics questions, when you were asking about dimensions you meant units right?

  20. anonymous
    • 5 years ago
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    yeah. I dint know how to put that question into english. And your right, i ment units.

  21. anonymous
    • 5 years ago
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    ok, I've heard units called dimensions before I was just making sure that's what you meant.

  22. anonymous
    • 5 years ago
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    In spanish we say dimension. I supposed it was the same in English. lol

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