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Math Help - Prove/show question

  1. #1
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    Prove/show question

    Heya!

    I've been struggling with this for some time now and would really appreciate some help. Need to show that the right side equals the left side.

    \frac{1}{sinx} = \frac{sinx}{1+cosx} + \frac{1}{tanx}


    Tried different ways to solve this but I get stuck each time.

    RS = Rightside; sorry if this is not the right way to type this. Not familiar with the english terms

    RS: \frac{sinx}{1+cosx} + \frac{1}{\frac{sinx}{cosx}}

    After this I've experimented with changing 1's to sin^2x+cos^2x among many other things.

    Honestly feels like I am really on the wrong track here. Mostly the 1+cosx that annoys me.

    Can someone shed some light on this for me? Thanks in advance!
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  2. #2
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    \frac{\sin{x}}{1+\cos{x}} + \frac{\cos{x}}{\sin{x}}

    \frac{\sin{x}}{1+\cos{x}} \cdot \frac{1-\cos{x}}{1-\cos{x}} + \frac{\cos{x}}{\sin{x}}<br />

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

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

    \frac{1-\cos{x}}{\sin{x}} + \frac{\cos{x}}{\sin{x}}

    \frac{1 - \cos{x} + \cos{x}}{\sin{x}}

    \frac{1}{\sin{x}}
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  3. #3
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    Thank you skeeter.

    Didn't realize 1/tan = cotx = cosx/sinx. When knowing this it was pretty simple. Cheers!
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