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denniel

  • 2 years ago

Prove this identity sin(2A)=2sinAcosA.

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  1. Tonks
    • 2 years ago
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    Start by considering 2A as A+A ... does that make you think of any particular theorem?

  2. TuringTest
    • 2 years ago
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    ...of course that makes me want to know how to prove the theorem you are thinking of @Tonks

  3. muhammad9t5
    • 2 years ago
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    sin(a+a)=sinacosb+cosasinb put the value of a and be here.

  4. micahwood50
    • 2 years ago
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    We know that sin(2A) = sin(A + A) sin (A + A) = cosA sinA + cosA sinA = 2 sinA cosA QED

  5. Tonks
    • 2 years ago
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    @TuringTest try stacking triangles in the unit circle... or is that for cosine?

  6. TuringTest
    • 2 years ago
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    I know it was some geometric proof like that, I don't remember those darn things...

  7. micahwood50
    • 2 years ago
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    Is that enough or do you need proof for sin (A + B) = cosA sinB + cosB sinA

  8. micahwood50
    • 2 years ago
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    http://youtu.be/BlEtOG4NRsg

  9. muhammad9t5
    • 2 years ago
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    formula you have given is wrong @micahwood50

  10. TuringTest
    • 2 years ago
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    it's correct

  11. micahwood50
    • 2 years ago
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    For proof of sin (A + B) = cosA sinB + cosB sinA: http://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities#Sine

  12. muhammad9t5
    • 2 years ago
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    http://upload.wikimedia.org/math/3/e/c/3ec0e99aa364deb052280bcd801fcec2.png

  13. TuringTest
    • 2 years ago
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    yep, that's the one...

  14. micahwood50
    • 2 years ago
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    @muhammad9t5 It's the same. Your point is?

  15. TuringTest
    • 2 years ago
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    perhaps you are neglecting the fact that multiplication is commutative muhammad?

  16. micahwood50
    • 2 years ago
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    |dw:1350147756505:dw|

  17. muhammad9t5
    • 2 years ago
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    ok i got it!! he has just rearranged the places of cos and sin.

  18. TuringTest
    • 2 years ago
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    in English that's called the commutative property of addition.

  19. muhammad9t5
    • 2 years ago
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    yup.

  20. micahwood50
    • 2 years ago
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    Yeah, sorry about that, though. It's easier for me to remember this formula this way.

  21. muhammad9t5
    • 2 years ago
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    @micahwood50 can this destroy the problem of sin(45-30) solve with your formula.

  22. muhammad9t5
    • 2 years ago
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    cos45*sin30-cos45sin30

  23. micahwood50
    • 2 years ago
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    Well, with minus, it's different story.

  24. muhammad9t5
    • 2 years ago
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    ok do sin(45+30)=cos45sin30+cos30sin45

  25. micahwood50
    • 2 years ago
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    Yeah, I got it. Thanks, though.

  26. muhammad9t5
    • 2 years ago
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    bro never mind if i disturb you! Accept just like the game of trig!

  27. micahwood50
    • 2 years ago
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    @muhammad9t5 I know the formulas, you don't have to correct me. Thanks, though.

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