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 11751 by tawa last updated on 31/Mar/17

$$\mathrm{Simplify}:\sin \left(6\theta \right)$$

Answered by mrW1 last updated on 31/Mar/17

$$\sin \left(6\theta \right)=\sin (4\theta +2\theta )=\sin \left(4\theta \right)\cos \left(2\theta \right)+\sin \left(2\theta \right)\cos \left(4\theta \right)$$$$=2\sin \left(2\theta \right){\cos }^2\left(2\theta \right)+\sin \left(2\theta \right)[1-{2\sin }^2\left(2\theta \right)]$$$$=2\sin \left(2\theta \right)[1-{\sin }^2\left(2\theta \right)]+\sin \left(2\theta \right)-{2\sin }^3\left(2\theta \right)$$$$=2\sin \left(2\theta \right)-{2\sin }^3\left(2\theta \right)+\sin \left(2\theta \right)-{2\sin }^3\left(2\theta \right)$$$$=3\sin \left(2\theta \right)-{4\sin }^3\left(2\theta \right)$$$$=3\times 2\sin \theta \cos \theta -4\times 8\times {\sin }^3\theta {\cos }^3\theta$$$$=2\sin \theta \cos \theta (3-{16\sin }^2\theta {\cos }^2\theta )$$

Commented by tawa last updated on 31/Mar/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com