Question Number 131097 by dw last updated on 01/Feb/21
![Determine the value of (S/π), if S is the sum, in radians, all equation solutions contained in the interval [0,14π]. the equation is: cos(x)+cos^5 (x)+cos(7x)=3](https://www.tinkutara.com/question/Q131097.png)
$${Determine}\:{the}\:{value}\:{of}\:\frac{{S}}{\pi},\:{if}\:{S}\:{is}\:{the}\:{sum},\:{in}\:{radians}, \\ $$$${all}\:{equation}\:{solutions}\:{contained}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{14}\pi\right]. \\ $$$$ \\ $$$${the}\:{equation}\:{is}: \\ $$$${cos}\left({x}\right)+{cos}^{\mathrm{5}} \left({x}\right)+{cos}\left(\mathrm{7}{x}\right)=\mathrm{3} \\ $$
Answered by MJS_new last updated on 01/Feb/21
![the only solution is cos x =1 ⇒ x=2nπ ⇒ S=2π(0+1+2+...+14)=210π ⇒ answer is 210](https://www.tinkutara.com/question/Q131098.png)
$$\mathrm{the}\:\mathrm{only}\:\mathrm{solution}\:\mathrm{is}\:\mathrm{cos}\:{x}\:=\mathrm{1} \\ $$$$\Rightarrow\:{x}=\mathrm{2}{n}\pi \\ $$$$\Rightarrow\:{S}=\mathrm{2}\pi\left(\mathrm{0}+\mathrm{1}+\mathrm{2}+…+\mathrm{14}\right)=\mathrm{210}\pi \\ $$$$\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{210} \\ $$
Commented by dw last updated on 01/Feb/21
![Sir^](https://www.tinkutara.com/question/Q131100.png)