Simplify trig expression?

Rewrite sin(x)/(1-sec(x)) without a fraction. Appraetnly answer is -cot(x)(cos(x)+1), but I don't know how to get there.

3 Answers

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  • 1 year ago

    sin(x)/(1 - sec(x))

    = -cos(x) cot(x/2)

  • TomV
    Lv 7
    1 year ago

    sin(x)/(1-sec(x))

    multiply top and bottom by 1+sec(x)

    = sin(x)(1+sec(x))/(1-sec²(x))

    multiply top and bottom by cos²(x) : recall cos(x)sec(x) = 1

    = sin(x)cos(x)(cos(x)+1)/(cos²(x) - 1)

    apply the Pythagorean Identity to the denominator

    = sin(x)cos(x)(cos(x) + 1)/(-sin²x)

    divide top and bottom by -sin(x)

    = -cos(x)(cos(x)+1)/sin(x)

    apply the identity cos(x)/sin(x) = cot(x)

    = -cot(x)(cos(x) + 1)

    QED

  • 1 year ago

    Multiply both top and bottom by (1+sec(x))

    The denominator reduces to (1²-sec²(x))

    Then multiply both top and bottom by cos²(x)

    The denominator then reduces to cos²(x)-1 which equals (-sin²(x))

    I'll let you do the rest for yourself.

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