If A, B, C are the angles of a $$\triangle\ ABC$$ then the following is equal to; $$\sin \left(\frac{B+C}{2}\right)$$
$$\sin\left(\frac{\ B+C}{2}\right)=\sin\left(\frac{\ 180-A}{2}\right)$$  since $$A+B+C=180^{\circ\ }$$
$$=\sin\left(90-\frac{\ A}{2}\right)$$
$$=\cos\frac{\ A}{2}$$
Hence, the correct answer is Option C
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