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Math Help - Proving Trig Identities

  1. #1
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    Proving Trig Identities

    I need help proving this Trig Identity:

    sin2(x\2) = (tanx-sinx)/2tanx

    Thanks.
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  2. #2
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    Re: Proving Trig Identities

    Simplify the right-hand side to (1 - cos(x))/2, then use the formula for cos(2 * x/2).
    Thanks from ostheimerdl
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  3. #3
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    Re: Proving Trig Identities

    Start with the right hand side. Wherever you see tanx replace it with sinx/cosx. Simplify what you get.
    The use the identity cosx=1-2sin^2x/2
    Thanks from ostheimerdl
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  4. #4
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    Re: Proving Trig Identities

    I am afraid I don't know the identity cosx=1-2sin^2x/2.
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  5. #5
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    Re: Proving Trig Identities

    Do you know the identity cos2x=1-2sin^2x? This is true any time the angle on the left hand side is twice the angle on the right hand side. Hence the identity I quoted.
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  6. #6
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    Re: Proving Trig Identities

    Okay, I see the identity you quoted. I must have made a mistake somewhere in calculations. After rewriting tan x as sin x / cos x and simplifying I end up with (1-sin x) / 2.
    Last edited by ostheimerdl; April 2nd 2012 at 10:25 AM.
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  7. #7
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    Re: Proving Trig Identities

    Quote Originally Posted by biffboy View Post
    Do you know the identity cos2x=1-2sin^2x?
    And if you are not sure, you should know the identity \cos2x=\cos^2x-\sin^2x, which together with \cos^2x+\sin^2x=1 gives \cos2x=1-2\sin^2x.
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  8. #8
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    Re: Proving Trig Identities

    Quote Originally Posted by ostheimerdl View Post
    After rewriting tan x as sin x / cos x and simplifying I end up with (1-sin x) / 2.
    \frac{\sin x}{\tan x}=\frac{\sin x}{\frac{\sin x}{\cos x}}=\frac{\sin x\cdot \cos x}{\sin x}=\cos x.
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  9. #9
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    Re: Proving Trig Identities

    You should have got (1-cosx)/2
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