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 29821 by Victor31926 last updated on 12/Feb/18

$$\frac{\sin 16\mathrm{x}}{\sin \mathrm{x}}?\mathrm{pls}\mathrm{help}.$$

Commented by abdo imad last updated on 13/Feb/18

$$whatisthequestion?$$

Commented by MJS last updated on 14/Feb/18

$$\frac{\sin 2nx}{\sin x}=2\underset{i=1}{\sum ^n}\cos (2i-1)x$$$$\frac{\sin (2n-1)x}{\sin x}=1+2\underset{i=1}{\sum ^{n-1}}\cos 2ix$$

Commented by Rasheed.Sindhi last updated on 14/Feb/18

$$\frac{\sin \left(2^{\mathrm{n}}\mathrm{x}\right)}{\sin \mathrm{x}}=2^{\mathrm{n}}\cos \mathrm{x}\cos 2\mathrm{x}\cos 4\mathrm{x}...\cos 2^{\mathrm{n}-1}\mathrm{x}$$$$=2^{\mathrm{n}}\underset{\mathrm{k}=0}{\stackrel{\mathrm{n}-1}{\mathrm{\Pi }}}\cos 2^{\mathrm{k}}\mathrm{x}$$

Answered by Rasheed.Sindhi last updated on 12/Feb/18

$$\frac{\sin 16\mathrm{x}}{\sin \mathrm{x}}=\frac{2\sin 8\mathrm{xcos}8\mathrm{x}}{\mathrm{sinx}}$$$$=\frac{2\left(2\sin 4\mathrm{xcos}4\mathrm{x}\right)\cos 8\mathrm{x}}{\mathrm{sinx}}$$$$=\frac{4\left(2\sin 2\mathrm{xcos}2\mathrm{x}\right)\cos 4\mathrm{xcos}8\mathrm{x}}{\mathrm{sinx}}$$$$=\frac{8\left(2\mathrm{sinxcosx}\right)\cos 2\mathrm{xcos}4\mathrm{xcos}8\mathrm{x}}{\mathrm{sinx}}$$$$=\frac{16\stackrel{\times }{\mathrm{sinx}cosxcos2xcos4xcos8x}}{\stackrel{\times }{\mathrm{sinx}}}$$$$=16\mathrm{cosxcos}2\mathrm{xcos}4\mathrm{xcos}8\mathrm{x}$$

Commented by Victor31926 last updated on 12/Feb/18

$$\mathrm{thnks}\mathrm{a}\mathrm{lot}...\mathrm{are}\mathrm{u}\mathrm{sure}\mathrm{of}\mathrm{the}\mathrm{answer}\mathrm{sir}?$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com