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starwars18

  • one year ago

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

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  1. starwars18
    • one year ago
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    \[\frac{ \sin x }{ 1 - \cos x } + \frac{ \sin x }{ 1 + \cos x } = 2 \csc x\]

  2. dan815
    • one year ago
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    okay first thing to know is csc(x) = 1/sin(x)

  3. starwars18
    • one year ago
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    yes

  4. dan815
    • one year ago
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    you should simplify the left side, by multiplying both fracctions by the conjugate

  5. dan815
    • one year ago
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    1-cos(x) and 1+cos(x) are factors of 1-(cos(x))^2

  6. dan815
    • one year ago
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    and 1-cos^2(x) = sin^2(x) as sin^2(x) + cos^2(x) = 1 this identity comes from the unit circle

  7. dan815
    • one year ago
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    okay yep it is right 2/sin(x) = 2csc(x) should be the right answer

  8. starwars18
    • one year ago
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    so sin x * (1 + cos x) + sin^3 x

  9. starwars18
    • one year ago
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    so they all cancel out leaving 2 over sin x... i get it now

  10. anonymous
    • one year ago
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    2 / sin(x) is like saying 2 times 1 /sin(x) which mean 2 times csc(x) or 2 csc(x) since csc = 1/sin(x)

  11. starwars18
    • one year ago
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    yes, ty i got it. sorry i forgot to close the question!!!

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