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Thread: General solution of trigonometric function

  1. #1
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    General solution of trigonometric function

    For any real numbers x and y. Sinx = siny implies $\displaystyle n\pi + (-1)^ny, where n \in Z$



    If sinx = siny, then sinx -siny = 0
    or$\displaystyle 2cos\frac{x+y}{2}sin\frac{x-y}{2} = 0$

    $\displaystyle \Rightarrow cos\frac{x+y}{2} = 0 ; sin\frac{x-y}{2}=0$



    Therefore $\displaystyle \frac{x+y}{2} = (2n+1)\frac{\pi}{2} or \frac{x-y}{2} = n\pi,$ where $\displaystyle n \in Z$



    i.e. X = $\displaystyle (2n+1)\pi -y or x = 2n\pi +y$, where $\displaystyle n \in Z$


    Please guide further.....
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  2. #2
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    Re: General solution of trigonometric function

    since you have found (x+y)/2 and (x-y)/2 make two similtaneous equations and solve them for x ,y it is easy .
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