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Math Help - Homework help

  1. #1
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    Homework help

    Can somebody help me simplify this?
    (cos2x+sin^2x)/(cos^2x)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by unmcintosh View Post
    Can somebody help me simplify this?
    (cos2x+sin^2x)/(cos^2x)
    \frac{cos(2x) + sin^2(x)}{cos^2(x)}

    = \frac{(2~cos^2(x) - 1) + sin^2(x)}{cos^2(x)}

    Upon some rearranging in the numerator:
    \frac{(cos^2(x) + sin^2(x)) + cos^2(x) - 1}{cos^2(x)}

    \frac{1 + cos^2(x) - 1}{cos^2(x)}

    \frac{cos^2(x)}{cos^2(x)}

    = 1

    -Dan
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  3. #3
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    thanks for the help and everything, but could you or someone else explain how you got from the first step to the second please?
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by unmcintosh View Post
    thanks for the help and everything, but could you or someone else explain how you got from the first step to the second please?
    cos(2x) = 2~cos^2(x) - 1

    We also have that
    cos(2x) = 1 - 2~sin^2(x) = cos^2(x) - sin^2(x)
    as well.

    See here.

    -Dan
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  5. #5
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    thank you. my test is tomorrow so im basically screwed. Also, could somebody help me verify
    -2cos^2xtan(-x)=sin2x
    please?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by unmcintosh View Post
    thank you. my test is tomorrow so im basically screwed. Also, could somebody help me verify
    -2cos^2xtan(-x)=sin2x
    please?
    -2\cos^2x\tan(-x)=\sin(2x)

    \implies -2\cos^2x\frac{\sin(-x)}{\cos(-x)}=\sin(2x)

    \implies -2\cos^2x\frac{-\sin(x)}{\cos(x)}=\sin(2x)

    \implies -2\cos(x)(-\sin(x))=\sin(2x)

    \implies 2\sin(x)\cos(x)=\sin(2x)

    This is the case, for this is a double angle identity.

    Hope this helped!
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