Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 88567 by jagoll last updated on 11/Apr/20

$$(1+\cos \frac{\pi }{11})(1+\cos \frac{3\pi }{11})(1+\cos \frac{5\pi }{11})(1+\cos \frac{7\pi }{11})(1+\cos \frac{9\pi }{11})$$

Commented by jagoll last updated on 11/Apr/20

$$\mathrm{T}=\left(2\cos {}^2\left(\frac{\pi }{22}\right)\right)\left({2\cos }^2\left(\frac{3\pi }{22}\right)\right)\left(2\cos {}^2\left(\frac{5\pi }{22}\right)\right)$$$$\left(2\cos {}^2\left(\frac{7\pi }{22}\right)\right)\left(2\cos {}^2\left(\frac{9\pi }{22}\right)\right)$$$$=32{\left[\cos \frac{\pi }{22}\cos \frac{3\pi }{22}\cos \frac{5\pi }{22}\cos \frac{7\pi }{22}\cos \frac{9\pi }{22}\right]}^2$$$$\cos \left(\frac{(2\mathrm{k}-1)\pi }{22}\right)=-\cos (\pi -\left(\frac{(2\mathrm{k}-1)\pi }{22}\right))$$$$\mathrm{T}=-32\cos \left(\frac{22-(2\mathrm{k}-1)}{22}\pi \right)$$$$\mathrm{tobe}\mathrm{continue}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com