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Math Help - Proving Identities problem

  1. #1
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    Proving Identities problem

    Hi will someone please help me with thease two problems.

    The book says

    Prove the identity: 1 + cscx/ secx = cosx + cotx

    and

    1 - 2 secx - 3secx^2x/ -tanx^2 = 1 - 3secx/ 1 - secx

    Thanks and explanation and final answer would be great.
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  2. #2
    Super Member bigwave's Avatar
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    Prove the identity:   1 + cscx/ secx = cosx + cotx

    \cos{x} = 1 when x=0

    \cos{x} +  \frac{\frac{1}{\sin{x}}}{\frac{1}{\cos{x}}} = \cos{x} + \cot{x}

    so

    \cos{x} + \cot{x} = \cos{x} + \cot{x}

    on the next one ... is this equation correct as given
    before we see if it can be proved

    1 - 2 secx - 3secx^2x/ -tanx^2 = 1 - 3secx/ 1 - secx

    1 - 2 \sec{x} - \frac{3\sec^{2x}{x}}{ -\tan^2{x}} = 1 - \frac{3\sec{x}}{1 - \sec{x}}
    Last edited by bigwave; December 22nd 2009 at 10:08 PM.
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  3. #3
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    this equation is right except for

    its supposed to be sec squared of x. I typed it wrong on the initial question my bad.
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  4. #4
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    Hello, BHSKid!

    Use parentheses please . . . or learn to use LaTeX.


    Prove: .(1 + csc x)/(sec x) = cos x + cot x

    We have: . \frac{1 + \csc x}{\sec x} \;=\;\frac{1}{\sec x} + \frac{\csc x}{\sec x} \;=\;\cos x + \frac{\frac{1}{\sin x}}{\frac{1}{\cos x}} \;=\;\cos x + \frac{\cos x}{\sin x} \;=\;\cos x + \cot x




    (1 - 2 sec x - 3 secx^2x)/(-tanx^2) = (1 - 3sec x)/(1 - sec x)

    We have: . \frac{1 - 2\sec x - 3\sec^2\!x}{-\tan^2\!x} \;=\;\frac{(1+\sec x)(1-3\sec x)}{1 - \sec^2\!x} \;=\;\frac{(1+\sec x)(1-3\sec x)}{(1+\sec x)(1-\sec x)} . =\;\frac{1-3\sec x}{1 - \sec x}

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