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Math Help - Which Trigonemetric Identity do I need to use?

  1. #1
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    Which Trigonemetric Identity do I need to use?

    Hi all,

    I'm stuck with just one step now of a long problem.

    Basically, how do I get from

    (1+2sinx)(\frac{1}{2}-sinx)

    to

    2cos(x)^{2}-\frac{3}{2}

    I've been told I need to use just one trigonometric identity, but I honestly can't think of any that will do it?

    Many thanks.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Which Trigonemetric Identity do I need to use?

    Expand:
    (1+2\sin(x))\cdot \left(\frac{1}{2}-\sin(x)\right)

    Afterwards use the fact \sin^2(x)=1-\cos^2(x)
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  3. #3
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    Re: Which Trigonemetric Identity do I need to use?

    Thanks but now theirs just one part I can't get after expanding,

    how to get from

    (2sinx)(-sinx)

    to

    2cos(x)^{2}-2

    this is the only missing step now,

    many thanks again.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Which Trigonemetric Identity do I need to use?

    If you expand:
    (1+2\sin(x))\cdot \left(\frac{1}{2}-\sin(x)\right) then you get:
    \frac{1}{2}+\sin(x)-\sin(x)-2\sin^2(x)=\frac{1}{2}-2\sin^2(x)

    Use \sin^2(x)=1-\cos^2(x) so you get:
    =\frac{1}{2}-2(1-\cos^2(x))
    =...
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  5. #5
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    Re: Which Trigonemetric Identity do I need to use?

    Thank you so much,

    I really appreciate it.
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  6. #6
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    Re: Which Trigonemetric Identity do I need to use?

    Quote Originally Posted by Srengam View Post
    (1+2sinx)(\frac{1}{2}-sinx)
    to
    2cos(x)^{2}-\frac{3}{2}
    (1+2sinx)(\frac{1}{2}-sinx)=\frac{1}{2}-2\sin^2(x)
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: Which Trigonemetric Identity do I need to use?

    Quote Originally Posted by Srengam View Post
    Thank you so much,

    I really appreciate it.
    You're welcome!
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