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Question Number 13305 by prakash jain last updated on 18/May/17

$$\mathrm{Does}$$$$\sin \mathrm{A}=\sin \mathrm{B}$$$$\mathrm{imply}\sin \frac{\mathrm{A}}{2}=\sin \frac{\mathrm{B}}{2}?$$$$\mathrm{For}\mathrm{example}\mathrm{A}=\pi \mathrm{and}\mathrm{B}=-\pi ?$$

Answered by ajfour last updated on 18/May/17

$$A=n\pi +{(-1)}^{n}B$$$$when\sin A=\sin B;$$$$\sin \frac{A}{2}=\sin (\frac{n\pi }{2}+{(-1)}^n\frac{B}{2})$$$$forB=-\pi ;A=\pi wehaven=2$$$$\sin \frac{A}{2}=\sin (\frac{2\pi }{2}+{(-1)}^2\frac{\mathit{B}}{2})$$$$\sin \frac{A}{2}=\sin (\pi +\frac{\mathit{B}}{2})\ne \sin \frac{\mathit{B}}{2}.$$

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