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Math Help - How do I simplify these things?!

  1. #1
    Junior Member
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    How do I simplify these things?!

    Big numbers like the 2 are to the power of:

    1. tan x * cos x

    2.csc x *cos x * tan x
    3. (1 - sin x) (1 + sin x)
    4. sin x + cos x * tan x
    5. cos2x-1
    _____________
    cos2x
    6.cos x * sin x * 1
    ___
    csc x
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  2. #2
    Member
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    Auckland, New Zealand
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    I'll help you get started but you can do the full simplifications.

    1. \tan{x} \times\cos{x} = \frac{\sin{x}}{\cos{x}} \times \cos{x} = \sin{x}

    2. \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\cos{x}} \times \frac{\sin{x}}{\cos{x}} \times \cos{x}

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

    4. = \sin{x} + \sin{x} = 2\sin{x}

    5. \frac{\cos^2{x} - 1}{\cos^2{x}} = \frac{1 - \sin^2{x} - 1}{\cos^2{x}} = -\frac{\sin^2{x}}{\cos^2{x}} = -\tan^2{x}

    6. \cos{x} \times \sin{x} \times \csc{x} = \cos{x} \times \sin{x} \times \frac{1}{\sin{x}}
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  3. #3
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    Quote Originally Posted by nzmathman View Post
    I'll help you get started but you can do the full simplifications.

    1. \tan{x} \times\cos{x} = \frac{\sin{x}}{\cos{x}} \times \cos{x} = \sin{x}

    2. \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\cos{x}} \times \frac{\sin{x}}{\cos{x}} \times \cos{x}

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

    4. = \sin{x} + \sin{x} = 2\sin{x}

    5. \frac{\cos^2{x} - 1}{\cos^2{x}} = \frac{1 - \sin^2{x} - 1}{\cos^2{x}} = -\frac{\sin^2{x}}{\cos^2{x}} = -\tan^2{x}

    6. \cos{x} \times \sin{x} \times \csc{x} = \cos{x} \times \sin{x} \times \frac{1}{\sin{x}}
    ------------------------------------------------------------------
    2. \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\sin{x}} \times \cos{x} \times \frac{\sin{x}}{\cos{x}} = ?
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  4. #4
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    the two cos's cancel out and then the two sin's cancel out so the answer is one
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  5. #5
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    Quote Originally Posted by j0nath0n3 View Post
    ------------------------------------------------------------------
    2. \csc{x} \times \cos{x} \times \tan{x} = \frac{1}{\sin{x}} \times \cos{x} \times \frac{\sin{x}}{\cos{x}} = ?

    \csc{x}= \frac{1}{\sin{x}} not   \frac{1}{\cos{x}}
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