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Math Help - trig identities

  1. #1
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    trig identities

    Verify the given identities : (for this post the letter T will = angle theyta)

    a) Sin 3T = 3 sinT - 4 sin^3T (hint 3T=2T+T)
    b) cos 3T = 4cos^3T-3cosT

    I used the trig identites I know to break them down, but I couldnt get it to the form of a and b. for example, for A I got this :

    sin3T = sin(2T+T) = sin2t x cosT + cos2T x sinT =
    1. (2sinT x cosT)cosT + (cos^2(T) - sin^2(t))sinT =
    2. 2sinTcosT^2 + sin(T)cos^2(T)-sin^3(T) =
    3. sin(T) (sin(T)cos^2(T) +cos^2(T)-sin^2(T))
    But I get stuck at 3. Dont see how he gets 3sinT-4sin^3T as the answer. same problem with problem B. Can someone show me the light?
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  2. #2
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    Quote Originally Posted by frankinaround View Post
    Verify the given identities : (for this post the letter T will = angle theyta)

    a) Sin 3T = 3 sinT - 4 sin^3T (hint 3T=2T+T)
    b) cos 3T = 4cos^3T-3cosT

    I used the trig identites I know to break them down, but I couldnt get it to the form of a and b. for example, for A I got this :

    sin3T = sin(2T+T) = sin2t x cosT + cos2T x sinT =
    1. (2sinT x cosT)cosT + (cos^2(T) - sin^2(t))sinT =
    2. 2sinTcosT^2 + sin(T)cos^2(T)-sin^3(T) =
    3. sin(T) (sin(T)cos^2(T) +cos^2(T)-sin^2(T))
    But I get stuck at 3. Dont see how he gets 3sinT-4sin^3T as the answer. same problem with problem B. Can someone show me the light?
    At line 2, you could factor out the sinT

    2sinTcos^2T+sinTcos^2T-sin^3T=sinT\left(2cos^2T+cos^2T\right)-sin^3T

    =sinT\left(3cos^2T\right)-sin^3T=3sinT\left(1-sin^2T\right)-sin^3T
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  3. #3
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    Quote Originally Posted by Archie Meade View Post
    At line 2, you could factor out the sinT

    2sinTcos^2T+sinTcos^2T-sin^3T=sinT\left(2cos^2T+cos^2T\right)-sin^3T

    =sinT\left(3cos^2T\right)-sin^3T=3sinT\left(1-sin^2T\right)-sin^3T
    Hey what trig identity did you use to change 3sinTcos^2T into 3sinT(1-sin^2T) ?
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  4. #4
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    Quote Originally Posted by frankinaround View Post
    Hey what trig identity did you use to change 3sinTcos^2T into 3sinT(1-sin^2T) ?
    It's a very fundamental one, you'd need to remember it well
    (it comes from Pythagoras' Theorem).

    cos^2T+sin^2T=1

    \Rightarrow\ cos^2T=1-sin^2T
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