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anonymous

  • one year ago

*Trigonometric Identities*

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  1. anonymous
    • one year ago
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    cos2 y − sin2 y = 1 − 2sin2 y

  2. anonymous
    • one year ago
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    its cos^2y - sin^2y= 1 - 2sin^2y

  3. welshfella
    • one year ago
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    try using the identity sin^2 y + cos^2 y = 1

  4. anonymous
    • one year ago
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    so change cos^2?

  5. anonymous
    • one year ago
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    sin^y = 1 - cos^2y

  6. anonymous
    • one year ago
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    isnt it better to change cos so ill have all sin?

  7. welshfella
    • one year ago
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    replace cos^2 y by 1 - sin^2 y on the left side

  8. anonymous
    • one year ago
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    so its (1 - sin^2y) - sin^2y = 1- 2sin^2y

  9. welshfella
    • one year ago
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    yes

  10. anonymous
    • one year ago
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    1- 2sin^2y = 1-2siny

  11. welshfella
    • one year ago
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    easy one this

  12. anonymous
    • one year ago
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    huh?

  13. welshfella
    • one year ago
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    - your last post was incorrect the previous one completed the proof

  14. anonymous
    • one year ago
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    but shouldnt both sides be the same thing?o.O

  15. welshfella
    • one year ago
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    No you have taken the left side and by using known trig identity converted it to the right side

  16. welshfella
    • one year ago
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    - therefore the identity is true

  17. anonymous
    • one year ago
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    1 - sin^2y) - sin^2y = 1- 2sin^2y

  18. anonymous
    • one year ago
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    from here I expanded the brackets and got 1 - sin^2y - sin^2y = 1- 2sin^2y

  19. anonymous
    • one year ago
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    - sin^2y - sin^2y = - 2 sin^2y

  20. anonymous
    • one year ago
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    right??

  21. welshfella
    • one year ago
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    cos^2y - sin^2y = 1 - 2sin^2y now cos^2 y = 1 - sin^2 y so substituting 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS

  22. welshfella
    • one year ago
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    yes

  23. welshfella
    • one year ago
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    RHS = right hand side

  24. anonymous
    • one year ago
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    so then wouldnt it be 1 - 2sin^2y = 1 - 2sin^2y??

  25. welshfella
    • one year ago
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    no - no need to write that usually with these , you pick the more complicated side of the identity and try to convert it to the other side . Once that is done you have confirmed the identity.

  26. anonymous
    • one year ago
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    so wat will the answer be then? o.O

  27. welshfella
    • one year ago
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    just write what i have put or if you like at the end write 'the above proves the original identity'.

  28. welshfella
    • one year ago
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    - thats what this is - a Proof.

  29. anonymous
    • one year ago
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    so this is the answer? 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS

  30. welshfella
    • one year ago
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    No there are 2 lines before that - check 6 posts back.

  31. welshfella
    • one year ago
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    the answer is the whole process of proving the identity

  32. welshfella
    • one year ago
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    cos^2y - sin^2y = 1 - 2sin^2y now cos^2 y = 1 - sin^2 y so substituting 1 - sin^2 y - sin^2 y = 1 - 2 sin^2 y = RHS The above proves the original identity

  33. welshfella
    • one year ago
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    you could also make a note to clarify that RHS = right hand side

  34. welshfella
    • one year ago
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    gotta go - hope this has clarified things

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