Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 176891 by Shrinava last updated on 27/Sep/22

Answered by mr W last updated on 27/Sep/22

sin x cos 3x (1/2)=2 sin x cos x (((cos x)/2)+(((√3) sin x)/2))(((cos x)/2)−(((√3) sin x)/2)) cos 3x = cos x (cos^2 x−3 sin^2 x) 4 cos^2 x−3 = cos^2 x−3 sin^2 x 3−3 =0 0=0 ✓ ⇒any x fulfills the equation and is a solution.

$$\mathrm{sin}\:{x}\:\mathrm{cos}\:\mathrm{3}{x}\:\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\frac{\mathrm{cos}\:{x}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}}{\mathrm{2}}\right)\left(\frac{\mathrm{cos}\:{x}}{\mathrm{2}}−\frac{\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}}{\mathrm{2}}\right) \\ $$$$\mathrm{cos}\:\mathrm{3}{x}\:=\:\mathrm{cos}\:{x}\:\left(\mathrm{cos}^{\mathrm{2}} \:{x}−\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:{x}\right) \\ $$$$\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:{x}−\mathrm{3}\:=\:\mathrm{cos}^{\mathrm{2}} \:{x}−\mathrm{3}\:\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$$$\mathrm{3}−\mathrm{3}\:=\mathrm{0} \\ $$$$\mathrm{0}=\mathrm{0}\:\checkmark \\ $$$$\Rightarrow{any}\:{x}\:{fulfills}\:{the}\:{equation}\:{and}\:{is} \\ $$$${a}\:{solution}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com