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Math Help - Simplify

  1. #1
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    Simplify

    I have been teaching myself calculus and in the process came across this equation:- 1/2*sin x/2*cos x/2. Can somebody show me how to simplify it? I am sure it involves the identity sin 2x=2*sin x*cos x.
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    Quote Originally Posted by p75213 View Post
    I have been teaching myself calculus and in the process came across this equation:- 1/2*sin x/2*cos x/2. Can somebody show me how to simplify it? I am sure it involves the identity sin 2x=2*sin x*cos x.
    Are you asking to simplify

    \frac{1}{2}\sin{\frac{x}{2}}\cos{\frac{x}{2}}?

    Yes, you do use the identity \sin{2\theta} = 2\sin{\theta}\cos{\theta}.


    If you let \theta = \frac{x}{2}

    we have \frac{1}{2}\sin{\theta}\cos{\theta}

     = \frac{1}{4}\cdot 2\sin{\theta}\cos{\theta}

     = \frac{1}{4}\sin{2\theta}

     = \frac{1}{4}\sin{\frac{2x}{2}}

     = \frac{1}{4}\sin{x}.
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    Many Thanks for the quick response.

    I won't tell you how long I stuffed around with this. Tricky little bugger - but not so difficult when somebody shows you how. Text books that just give you the answer without showing you how it was arrived at drive me nuts.
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  4. #4
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    Can you buy a solutions book that goes with your text book?
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  5. #5
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    The solutions are given but sometimes the workings are very brief (important chunks missed out). In most cases I have been able to figure it out with the help of google. However it would be a time saver if everything was in the answer given without having to go searching on the internet.
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