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anonymous

  • one year ago

Verify the identity. cos(4u) = cos^2(2u) - sin^2(2u)

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  1. anonymous
    • one year ago
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    \[\cos \left( 4u\right) = \cos ^{2}\left( 2u \right) - \sin ^{2}\left( 2u \right)\]

  2. anonymous
    • one year ago
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    @Luigi0210

  3. anonymous
    • one year ago
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    @Hero

  4. anonymous
    • one year ago
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    @arindameducationusc

  5. anonymous
    • one year ago
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    @kaitlyn_nicole

  6. anonymous
    • one year ago
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    @kaitlyn_nicole

  7. anonymous
    • one year ago
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    @Michele_Laino

  8. arindameducationusc
    • one year ago
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    Do you know Cos2theta= cos^2theta-sin^2theta?

  9. anonymous
    • one year ago
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    yes, double angle identity

  10. Michele_Laino
    • one year ago
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    hint: we can rewrite the left side as below: \[\Large \cos \left( {4u} \right) = \cos \left( {2u + 2u} \right)\]

  11. Michele_Laino
    • one year ago
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    now you can apply the formula of addition for cosine function

  12. Michele_Laino
    • one year ago
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    \[\Large \cos \left( {x + y} \right) = \cos x\cos y - \sin x\sin y\]

  13. anonymous
    • one year ago
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    cos ( 2u + 2u ) = cos (2u) cos (2u) - sin (2u) sin (2u) ?

  14. Michele_Laino
    • one year ago
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    that's right!

  15. anonymous
    • one year ago
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    what do i do from there?

  16. Michele_Laino
    • one year ago
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    it is simple, since: \[\Large \cos \left( {2u} \right)\cos \left( {2u} \right) = {\left( {\cos \left( {2u} \right)} \right)^2}\]

  17. Michele_Laino
    • one year ago
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    similarly for sin(2u)*sin(2u)

  18. anonymous
    • one year ago
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    sin(2u) sin(2u) = (sin(2u))^2 ?

  19. Michele_Laino
    • one year ago
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    yes!

  20. anonymous
    • one year ago
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    okay, so since im trying to verify this identity, what else do i do to get the answer to look like cos(4u) = cos(4u) ?

  21. Michele_Laino
    • one year ago
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    since we have proven that left side is equal to right side, then we are done here

  22. anonymous
    • one year ago
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    so is the final answer cos ( 2u + 2u ) = cos (2u) cos (2u) - sin (2u) sin (2u) or cos(2u) cos(2u) = (cos(2u))^2 ?

  23. Michele_Laino
    • one year ago
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    the answer is the entire procedure which shows how to get the right side, starting from left side

  24. anonymous
    • one year ago
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    ahhhhhh, i see, i see. thank you soooooo much for your help!

  25. Michele_Laino
    • one year ago
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    :)

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