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ChristopherW28 Group Title

Verify that (1-cos^2x)(1+cos^2x)=2sin^2x-sin^4x is a trig identity

  • 10 months ago
  • 10 months ago

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  1. myininaya Group Title
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    By a certain Pythagorean identity we can say 1-cos^2(x)=?

    • 10 months ago
  2. ChristopherW28 Group Title
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    Sin^2x?

    • 10 months ago
  3. myininaya Group Title
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    yep! :)

    • 10 months ago
  4. myininaya Group Title
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    so this means we now have \[\sin^2(x)(1+\cos^2(x))=2\sin^2(x)-\sin^4(x)\] now this is an identity we are trying to prove now we have one side in terms of sin and another side in terms of mixture of sin and cos

    • 10 months ago
  5. myininaya Group Title
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    We could use that same identity to rewrite cos^2(x)

    • 10 months ago
  6. myininaya Group Title
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    \[1-\cos^2(x)=\sin^2(x) => \cos^2(x)=\]

    • 10 months ago
  7. myininaya Group Title
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    that is a blank for you to fill in

    • 10 months ago
  8. ChristopherW28 Group Title
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    I'm lost

    • 10 months ago
  9. myininaya Group Title
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    Ok I want to rewrite cos^2(x) because the other side is just in terms of sin I know an identity that has cos^2(x) and sin^2(x) in it.

    • 10 months ago
  10. myininaya Group Title
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    \[\cos^2(x)+\sin^2(x)=1 \]

    • 10 months ago
  11. myininaya Group Title
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    So cos^2(x)=?

    • 10 months ago
  12. ChristopherW28 Group Title
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    Sin^x+ 1

    • 10 months ago
  13. myininaya Group Title
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    1-sin^2(x)

    • 10 months ago
  14. ChristopherW28 Group Title
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    Sin^2x+1?

    • 10 months ago
  15. ChristopherW28 Group Title
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    I was close

    • 10 months ago
  16. myininaya Group Title
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    1-cos^2(x)=sin^2(x) 1-sin^2(x)=cos^2(x) cos^2(x)+sin^2(x)=1

    • 10 months ago
  17. myininaya Group Title
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    So we can back to what we are trying to prove and replace the cos^2(x) with 1-sin^2(x) \[\sin^2(x)(1+(1-\sin^2(x))=2\sin^2(x)-\sin^4(x)\]

    • 10 months ago
  18. myininaya Group Title
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    I replaced mr.cos^2(x) with mrs. (1-sin^2(x))

    • 10 months ago
  19. myininaya Group Title
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    now we don't need those parenthesis since there is a + in front of that parenthesis lets drop that extra stuff giving us: \[\sin^2(x)(1+1-\sin^2(x))=2\sin^2(x)-\sin^4(x) \]

    • 10 months ago
  20. myininaya Group Title
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    now 1+1=2 which I know you know (:p) so now you distribute on that left hand side

    • 10 months ago
  21. ChristopherW28 Group Title
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    I gtg I can figure out what's left. Friend me on Facebook @ Christopher McElhannon. I will need your help again :)

    • 10 months ago
  22. myininaya Group Title
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    I will be here most likely. I'm not much of a facebook user. I'm on facebook free diet right now. :p

    • 10 months ago
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