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anonymous

  • one year ago

(sin Θ − cos Θ)2 − (sin Θ + cos Θ)2

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  1. anonymous
    • one year ago
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    −4sin(Θ)cos(Θ) 2 sin2 Θ cos2 Θ

  2. dumbcow
    • one year ago
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    distribute, then combine terms note : sin^2 + cos^2 = 1

  3. UnkleRhaukus
    • one year ago
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    use difference of squares, a^2 - b^2 = (a+b)(a-b)

  4. midhun.madhu1987
    • one year ago
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    \[a ^{2} - b ^{2} = (a-b)(a+b)\]

  5. UnkleRhaukus
    • one year ago
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    where a = sin Θ − cos Θ b = sin Θ + cos Θ

  6. UnkleRhaukus
    • one year ago
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    can you do it @gabbimanges17 ?

  7. anonymous
    • one year ago
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    @UnkleRhaukus is the answer sin^2?

  8. UnkleRhaukus
    • one year ago
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    nope. what do you get for (a-b)? and what do you get for (a+b)?

  9. anonymous
    • one year ago
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    @UnkleRhaukus im not sure

  10. UnkleRhaukus
    • one year ago
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    \[ (\sin\theta − \cos\theta)^2 − (\sin\theta + \cos\theta)^2\] \[\Big((\sin\theta − \cos\theta)+(\sin\theta + \cos\theta)\Big)\Big((\sin\theta − \cos\theta)-(\sin\theta + \cos\theta)\Big)\]

  11. anonymous
    • one year ago
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    looks like they cancel each other out

  12. UnkleRhaukus
    • one year ago
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    many of the terms cancel away, but not all of them

  13. anonymous
    • one year ago
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    @UnkleRhaukus can you specify?

  14. UnkleRhaukus
    • one year ago
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    \[\color{teal}{(\sin\theta − \cos\theta)}^2 − \color{orange}{(\sin\theta + \cos\theta)}^2\] \[=\Big(\color{teal}{(\sin\theta − \cos\theta)}+\color{orange}{(\sin\theta + \cos\theta)}\Big)\Big(\color{teal}{(\sin\theta − \cos\theta)}-\color{orange}{(\sin\theta + \cos\theta)}\Big)\\ =\Big(\sin\theta − \cos\theta+\sin\theta + \cos\theta\Big)\Big(\sin\theta − \cos\theta-\sin\theta - \cos\theta\Big)\\ = \]

  15. UnkleRhaukus
    • one year ago
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    \[=\Big(\sin\theta +\sin\theta + \cos\theta − \cos\theta\Big)\Big(\sin\theta -\sin\theta - \cos\theta− \cos\theta\Big)\\ =\]

  16. anonymous
    • one year ago
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    0

  17. UnkleRhaukus
    • one year ago
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    work it out properly

  18. anonymous
    • one year ago
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    im not sure what youre asking.. it looks like the last two cos dont cancel out

  19. UnkleRhaukus
    • one year ago
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    \[=\Big(\sin\theta +\sin\theta + \cos\theta − \cos\theta\Big)\Big(\sin\theta -\sin\theta - \cos\theta− \cos\theta\Big)\\ =\Big((1+1)\sin\theta + (1-1)\cos\theta\Big)\Big((1-1)\sin\theta +(-1-1)\cos\theta\Big)\\ =\]

  20. anonymous
    • one year ago
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    2?

  21. anonymous
    • one year ago
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    you have me in a twist

  22. UnkleRhaukus
    • one year ago
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    simplify!

  23. anonymous
    • one year ago
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    −4sin(Θ)cos(Θ)

  24. UnkleRhaukus
    • one year ago
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    are you sure?

  25. anonymous
    • one year ago
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    im not sure about anything anymore, please can you explain in plain english

  26. UnkleRhaukus
    • one year ago
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    The expression given is a difference of squares, we used a formula we already knew for the difference of square to rearrange the expression. Then we simplified the terms in this new form, and we got ...

  27. anonymous
    • one year ago
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    −4sin(Θ)cos(Θ)

  28. UnkleRhaukus
    • one year ago
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    good.

  29. anonymous
    • one year ago
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    thank you!

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