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Question Number 39028 by maxmathsup by imad last updated on 01/Jul/18

$$1)calculateA=cos\left(\frac{\pi }{7}\right).cos\left(\frac{2\pi }{7}\right).cos\left(\frac{3\pi }{7}\right)$$$$2)calculateB=tan\left(\frac{\pi }{7}\right).tan\left(\frac{2\pi }{7}\right).tan\left(\frac{3\pi }{7}\right).$$

Answered by tanmay.chaudhury50@gmail.com last updated on 02/Jul/18

$$A\times 2sin\frac{\mathrm{\Pi }}{7}=2sin\frac{\mathrm{\Pi }}{7}cos\frac{\mathrm{\Pi }}{7}cos\frac{2\mathrm{\Pi }}{7}cos\frac{3\mathrm{\Pi }}{7}$$$$A\times 2sin\frac{\mathrm{\Pi }}{7}=sin\frac{2\mathrm{\Pi }}{7}cos\frac{2\mathrm{\Pi }}{7}cos\frac{3\mathrm{\Pi }}{7}$$$$A\times 2^{2}sin\frac{\mathrm{\Pi }}{7}=sin\frac{4\mathrm{\Pi }}{7}cos\frac{3\mathrm{\Pi }}{7}$$$$A\times 2^{3}sin\frac{\mathrm{\Pi }}{7}=2sin\frac{4\mathrm{\Pi }}{7}cos\frac{3\mathrm{\Pi }}{7}$$$$A\times 2^{3}sin\frac{\mathrm{\Pi }}{7}=sin\mathrm{\Pi }+sin\frac{\mathrm{\Pi }}{7}$$$$A\times 2^{3}sin\frac{\mathrm{\Pi }}{7}=sin\frac{\mathrm{\Pi }}{7}$$$$A=\frac{1}{8}$$

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