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anonymous

  • one year ago

Simplify sin(45-x)cos(45-x)

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  1. Hero
    • one year ago
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    Used Sum and difference Angle formulas for sine and cosine to simplify

  2. anonymous
    • one year ago
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    So 2sinAcosB=sin(A+B)+sin(A-B)

  3. anonymous
    • one year ago
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    But how the question sin and cos become sin and sin in the forumla?

  4. Hero
    • one year ago
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    where'd you get that formula.

  5. anonymous
    • one year ago
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    My tudor

  6. anonymous
    • one year ago
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    Is it incorrect?

  7. Hero
    • one year ago
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    It doesn't look correct as written

  8. anonymous
    • one year ago
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    What's the correct formula?

  9. Hero
    • one year ago
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    http://regentsprep.org/Regents/math/algtrig/ATT14/formulalesson.htm

  10. anonymous
    • one year ago
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    Ohh, right

  11. anonymous
    • one year ago
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    So what formula do I use?

  12. anonymous
    • one year ago
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    Do I work with sin (45-x) separately and then cos (45-x) separately?

  13. Hero
    • one year ago
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  14. anonymous
    • one year ago
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    Yep, I understood that part

  15. anonymous
    • one year ago
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    I subbed in the values and got this:

  16. anonymous
    • one year ago
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    (sin45cosx-cos45sinx) (cos45cosx+sin45sinx)

  17. Hero
    • one year ago
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    You should know what Sin 45 and cos ( 45)

  18. anonymous
    • one year ago
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    Sin 45 is rt2/2

  19. anonymous
    • one year ago
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    And cos 45 is rt2/3

  20. Hero
    • one year ago
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    They're both sqrt(2)/2

  21. anonymous
    • one year ago
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    What about the x ?

  22. Hero
    • one year ago
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    You don't need to Know What x ls. You're simplifying an expression not solving an equation.

  23. anonymous
    • one year ago
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    Am I doing this wrong?

  24. Hero
    • one year ago
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    Yes

  25. Hero
    • one year ago
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    Okay

  26. Hero
    • one year ago
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  27. anonymous
    • one year ago
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    How do I further simplify this?

  28. Hero
    • one year ago
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    Algebraically

  29. anonymous
    • one year ago
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    So that becomes

  30. anonymous
    • one year ago
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    (rt2/2)^2 x (cosx-sinx)(cosx+sinx)

  31. Hero
    • one year ago
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    Just try to work on it and post your simplification

  32. anonymous
    • one year ago
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    = 1/2 x (cosx-sinx)(cosx+sinx)

  33. anonymous
    • one year ago
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    I don't know how to further simplify

  34. Hero
    • one year ago
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    There's no x after 1/2

  35. anonymous
    • one year ago
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    Oh that's a multiplication sign

  36. anonymous
    • one year ago
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    = 1/2(cosx-sinx)(cosx+sinx)

  37. anonymous
    • one year ago
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    That's a difference of two squares

  38. Hero
    • one year ago
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    correct

  39. anonymous
    • one year ago
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    =1/2(cosx-sinx)^2

  40. Hero
    • one year ago
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    Not written correctly

  41. Hero
    • one year ago
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    Do you want to try to correct your own Mistake?

  42. anonymous
    • one year ago
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    Is it 1/2 cosx^2-sin^2 ?

  43. Hero
    • one year ago
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    That's better

  44. anonymous
    • one year ago
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    Yep

  45. anonymous
    • one year ago
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    Ok, how do I further simplify?

  46. Hero
    • one year ago
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    sin(×) is the primitive trig expression So express the simplification in terms Of sine.

  47. anonymous
    • one year ago
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    ?

  48. anonymous
    • one year ago
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    What do you mean?

  49. Hero
    • one year ago
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    Do you know the Pythagorean identity?

  50. anonymous
    • one year ago
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    Yes

  51. anonymous
    • one year ago
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    sin^2x+cos^2x=1

  52. anonymous
    • one year ago
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    Could you please give me the completed working out, I'm a bit short on time

  53. Hero
    • one year ago
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    Isolate cos^2 x

  54. Hero
    • one year ago
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    We're almost done.

  55. anonymous
    • one year ago
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    And then..?

  56. Hero
    • one year ago
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    substitute cos ^2x with its equivalent expression then finish simplifying

  57. anonymous
    • one year ago
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    Ok thank you so much

  58. Hero
    • one year ago
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    By the way,

  59. anonymous
    • one year ago
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    Yes?

  60. Hero
    • one year ago
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