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Dimulai oleh CrisTaNa, Agustus 25, 2010, 08:03:29 PM

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CrisTaNa

jika \frac{\cos \alpha}{1-\sin \alpha}=a, nyatakan \tan \frac12 \alpha dalam a

Mtk Kerajaan Mataram

\frac{\cos \alpha}{1-\sin \alpha}=a

==> \frac{\(\cos \frac{\alpha}{2}\)^2-\(\sin \frac{\alpha}{2}\)^2}{\(\cos \frac{\alpha}{2}\)^2+\(\sin \frac{\alpha}{2}\)^2-2\sin \frac{\alpha}{2} \cos \frac{\alpha}{2}}=a

==> \frac{\(\cos \frac{\alpha}{2}-\sin \frac{\alpha}{2}\)\(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\)}{\(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\)\(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\)}=a

==> \frac{\(\cos \frac{\alpha}{2}-\sin \frac{\alpha}{2}\)}{\(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\)}=a

==> \frac{\frac{\(\cos \frac{\alpha}{2}-\sin \frac{\alpha}{2}\)}{\cos \frac{\alpha}{2}}}{\frac{\(\cos \frac{\alpha}{2}+\sin \frac{\alpha}{2}\)}{\cos \frac{\alpha}{2}}}=a

==> \frac{\(1-\tan \frac{\alpha}{2}\)}{\(1+\tan \frac{\alpha}{2}\)}=a

==> 1-\tan \frac{\alpha}{2}=a+a\tan \frac{\alpha}{2}

==> \tan \frac{\alpha}{2}=\frac{1-a}{1+a}

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