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**Trigonometric Identity??**

I just can't figure this out. I don't think i've covered enough material to do this. Can anyone help? I've put the entire question but im sure all i need is a little explanation and maybe the first answer and i could do the rest.

[tex] Let z = tan(\theta/2).// Show that

cos\theta = \frac{1-z^2}{1+z^2}

sin\theta = \frac{2z}{1+z^2}

\frac{d\theta}{dz} = \frac{2}{1+z^2}

[/tex]

Thanks. Sorry i tried to use latex but cant figure out spaces.

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