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Math Help - Two geometry equations

  1. #1
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    Two geometry equations

    How ?
    Attached Thumbnails Attached Thumbnails Two geometry equations-trigo.jpg  
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  2. #2
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    For Problem 1:
    Factor to get, call y=x-\frac{\pi}{5}
    \cos y (2\cos^2y-3\cos y-1)=0
    Thus,
    \cos y=0 or 2\cos^2y-3\cos y-1=0
    Solving the second equation with quadradic formula:
    \cos y=\frac{3\pm\sqrt{17}}{4}
    Thus,
    \cos y=0
    \cos y\approx 1.78--Impossible.
    \cos y\approx -.28
    Solve for y
    after that you can solve for x
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  3. #3
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    The product formula,
    \sin x\sin y=\frac{1}{2}[\cos(x-y)-\cos(x+y)]
    Thus,
    \sin (\pi/4+x)\sin (\pi/4-x)
    Can be expressed as,
    \frac{1}{2}[\cos(2x)-\cos(\pi/2)]
    But \cos(\pi/2)=0 thus,
    \frac{1}{2}\cos 2x=.33
    Thus,
    \cos 2x=.66
    Now you can solve for 2x for which you can solve for x
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