lim x->pi 1-sin^2x/(sin 1/2x - cos 1/2x)^2

[tex]1-\sin^{2}x=(1-\sin(x))(1+\sin(x))[/tex]
[tex](\sin(\frac{1}{2}x)-\cos(\frac{1}{2}x)) ^{2}=\sin^{2}(\frac{1}{2}x)-2\sin(\frac{1}{2}x) \cos(\frac{1}{2}x) + \cos^{2}(\frac{1}{2}x)))[/tex]
jadi
[tex]\lim\limits_{x \rightarrow \pi}\frac{1-\sin^{2}x}{(\sin(\frac{1}{2}x)-\cos(\frac{1}{2}x))^{2}}[/tex]
[tex]\lim\limits_{x \rightarrow \pi}\frac{(1-\sin(x))(1+\sin(x))}{1-\sin(x)}[/tex]
[tex]\lim\limits_{x \rightarrow \pi}1+\sin(x)[/tex]
[tex]=1+\sin(\pi)=0/tex]