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Simplify quotient of trignometric functions

  1. Mar 14, 2009 #1
    Simplify [tex]\frac{sinx + tanx}{cscx + cotx}[/tex]

    I start with [tex]\frac{sinx + tanx}{cscx + cotx} = \frac{sinx + \frac{sinx}{cosx}}{\frac{1}{sinx} + \frac{cosx}{sinx}} [/tex]

    At this point I am stuck, I cannot see how we then get from [tex]\frac{sinx + \frac{sinx}{cosx}}{\frac{1}{cosx} + \frac{cosx}{sinx}} = \frac{sinx cosx + sin x}{1} \times \frac{sin x}{cos x} [/tex]

    What happened to the [tex]\frac{1}{cos x}[/tex] from the denominator? I thought that would become [tex]\frac{cos x}{1}[/tex] to give [tex](sinx + \frac{sinx}{cosx}) \times ({\frac{cosx}{1} + \frac{sin x}{cos x})[/tex]
    Last edited: Mar 14, 2009
  2. jcsd
  3. Mar 14, 2009 #2
    I think I figured it out. Needed to simplify the numerator and denominator into a single fraction, then invert the denominator and multiply. This was the step I was missing. Also needed to factorise the result of the multiplication.
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