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Thread: Guysss i need help

  1. #1
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    Guysss i need help

    Verify:
    sin( pie / 2 - x) = cos x
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^
    Verify:
    sin( pie / 2 - x) = cos x
    The summation identity is:

    $\displaystyle \sin(A+B)=\sin(A) \cos(B)+\cos(A) \sin(B)$.

    Put $\displaystyle A=\pi/2$, and $\displaystyle B=-x$ giving:

    $\displaystyle \sin(\pi/2-x)=\sin(\pi/2) \cos(-x)+\cos(\pi/2) \sin(-x)$,

    but $\displaystyle \sin(\pi/2)=1$, and $\displaystyle \cos(\pi/2)=0$, so:

    $\displaystyle \sin(\pi/2+x)= \cos(-x)$.

    However $\displaystyle \cos$ is an even function so $\displaystyle \cos(-x)=\cos(x)$, hence:

    $\displaystyle \sin(\pi/2+x)= \cos(x)$.

    RonL
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