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 23243 by paro123 last updated on 27/Oct/17

2^(n−1) sin a×sin 2a×sin 3a×......×sin (n−1)a=n why?

$$\mathrm{2}^{\mathrm{n}−\mathrm{1}} \mathrm{sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}×\mathrm{sin}\:\mathrm{3a}×......×\mathrm{sin}\:\left(\mathrm{n}−\mathrm{1}\right)\mathrm{a}=\mathrm{n}\:\mathrm{why}? \\ $$

Commented by mrW1 last updated on 28/Oct/17

this statement is wrong! you can find a lot of examples: if n=3: 2^(3−1) sin a×sin 2a=4sin a×sin 2a≠3 if a=±π or ±(π/2) or ±(π/3) or ±(π/4).....: 2^(n−1) sin a×sin 2a×sin 3a×......×sin (n−1)a=0≠n

$$\mathrm{this}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{wrong}! \\ $$$$ \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{find}\:\mathrm{a}\:\mathrm{lot}\:\mathrm{of}\:\mathrm{examples}: \\ $$$$\mathrm{if}\:\mathrm{n}=\mathrm{3}: \\ $$$$\mathrm{2}^{\mathrm{3}−\mathrm{1}} \mathrm{sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}=\mathrm{4sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}\neq\mathrm{3} \\ $$$$ \\ $$$$\mathrm{if}\:\mathrm{a}=\pm\pi\:\mathrm{or}\:\pm\frac{\pi}{\mathrm{2}}\:\mathrm{or}\:\pm\frac{\pi}{\mathrm{3}}\:\mathrm{or}\:\pm\frac{\pi}{\mathrm{4}}.....: \\ $$$$\mathrm{2}^{\mathrm{n}−\mathrm{1}} \mathrm{sin}\:\mathrm{a}×\mathrm{sin}\:\mathrm{2a}×\mathrm{sin}\:\mathrm{3a}×......×\mathrm{sin}\:\left(\mathrm{n}−\mathrm{1}\right)\mathrm{a}=\mathrm{0}\neq\mathrm{n} \\ $$

Commented by paro123 last updated on 28/Oct/17

Terms of Service

Privacy Policy

Contact: info@tinkutara.com