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Math Help - Write the expressions in terms of cosine?

  1. #1
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    Write the expressions in terms of cosine?

    Q)Write the following expression in terms of cosine both in a simplified form?

     \frac{1-csc^2x}{csc^2x}

    Attempt- Is my attempt Correct )

     -1(sin^2x-1) =-cos^2x

    Thank you
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mj.alawami View Post
    Q)Write the following expression in terms of cosine both in a simplified form?

     \frac{1-csc^2x}{csc^2x}

    Attempt- Is my attempt Correct )

     -1(sin^2x-1) =-cos^2x

    Thank you
    csc^2(x) = \frac{1}{sin^2(x)}

    <br />
1- \frac{1}{sin^2(x)} = \frac{sin^2(x) - 1}{sin^2(x)}

    Overall the sum becomes:

     \frac{sin^2(x) - 1}{sin^2(x)csc(x)} and so the denominator will be sin(x)

    sin^2(x) - 1 = -cos^2(x) and sin(x) = \sqrt{1-cos^2(x)}

    therefore we have \frac{-cos^2(x)}{\sqrt{1-cos^2(x)}}

    -----------

    From your expression you can say that -1(sin^2(x)-1) = 1-sin^2(x) = cos^2(x)
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    Quote Originally Posted by e^(i*pi) View Post
    csc^2(x) = \frac{1}{sin^2(x)}

    <br />
1- \frac{1}{sin^2(x)} = \frac{sin^2(x) - 1}{sin^2(x)}

    Overall the sum becomes:

     \frac{sin^2(x) - 1}{sin^2(x)csc(x)} and so the denominator will be sin(x)

    sin^2(x) - 1 = -cos^2(x) and sin(x) = \sqrt{1-cos^2(x)}

    therefore we have \frac{-cos^2(x)}{\sqrt{1-cos^2(x)}}

    -----------

    From your expression you can say that -1(sin^2(x)-1) = 1-sin^2(x) = cos^2(x)
    -----------
    Your equation is correct but you can simplify the  csc^2 in the denominator to  \frac{1}{sin^2} and then you can cancel the numerator and get  sin^2-1

    But i am not sure of my attempt

    Thank you
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by mj.alawami View Post
    -----------
    Your equation is correct but you can simplify the  csc^2 in the denominator to  \frac{1}{sin^2} and then you can cancel the numerator and get  sin^2-1

    But i am not sure of my attempt

    Thank you
    My apologies I misread the question. Yes you can cancel the denominator because sin^2(x)csc^2(x) = 1
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