for \( \triangle A B C \) prove that
(i)
\[
\begin{array}{l}
\sin \frac{A}{2}+\sin \frac{B}{2}+...
for \( \triangle A B C \) prove that
(i)
\[
\begin{array}{l}
\sin \frac{A}{2}+\sin \frac{B}{2}+\sin \frac{C}{2}-1 \\
=4 \sin \frac{\pi-A}{4} \sin \frac{\pi-B}{4} \sin \frac{\pi-C}{4}
\end{array}
\]
(ii) \( \sin (B+2 C)+\sin (C+2 A)+\sin (A+2 B) \)
\[
=4 \sin \frac{B-C}{2} \sin \frac{C-A}{2} \sin \frac{A-B}{2}
\]
(iii) \( \sin (B+C-A)+\sin (C+A-B)+\sin (A+B-C)=4 \) \( \sin A \sin B \sin C \)
(iv) \( \cos \frac{A}{2}+\cos \frac{B}{2}-\cos \frac{C}{2} \)
\[
=4 \cos \frac{\pi-A}{4} \cos \frac{\pi-B}{4} \cos \frac{\pi-C}{4}
\]
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