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2.A + B + C = 180 prove that cos A/2 + cos B/2 + cos C/2 = 4cos(âˆ-A)/4 . cos(âˆ-B)/4 . cos(âˆ-C)/4
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11R.H.S = 4\ cos\ (\frac{\pi }{4} - \frac{A}{4})\ cos\ (\frac{\pi }{4} - \frac{B}{4})\ cos\ (\frac{\pi }{4} - \frac{C}{4})
= \frac{4}{\sqrt{2}\sqrt{2}\sqrt{2}} \left[cos\frac{A}{4}\ + Sin\ \frac{A}{4} \right]\left[cos\frac{B}{4}\ + Sin\ \frac{B}{4} \right]\left[cos\frac{C}{4}\ + Sin\ \frac{C}{4} \right]
= \sqrt{2} \left[Sin\ (\frac{A}{4}+\frac{B}{4}+\frac{C}{4}) + Cos\(\frac{A}{4}+\frac{B}{4}+\frac{C}{4}) \right]
= 2\ Sin\ (\frac{A}{2} + \frac{B}{2} + \frac{C}{2})
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