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Question Number 165851 by Bagus1003 last updated on 09/Feb/22

$$2{\left(\cos \left(45\right)\right)}^4=\frac{1}{2}\times \frac{\mathit{\tau }}{x\times 2}+1-\frac{2}{2}$$$$Howmuchthexis?$$

Answered by MJS_new last updated on 09/Feb/22

$$2{\left(\cos \left(45\right)\right)}^4=\frac{1}{2}\times \frac{\tau }{x\times 2}+1-\frac{2}{2}$$$$2{\left(\cos \left(45\right)\right)}^4-1+\frac{2}{2}=\frac{1}{2}\times \frac{\tau }{x\times 2}$$$$(2{\left(\cos \left(45\right)\right)}^4-1+\frac{2}{2})\mathbf{÷}\frac{1}{2}=\frac{\tau }{x\times 2}$$$$\frac{(2{\left(\cos \left(45\right)\right)}^4-1+\frac{2}{2})\mathbf{÷}\frac{1}{2}}{\tau }=\frac{1}{x\times 2}$$$$x\times 2\times \frac{(2{\left(\cos \left(45\right)\right)}^4-1+\frac{2}{2})\mathbf{÷}\frac{1}{2}}{\tau }=1$$$$x=\frac{1}{2\times \frac{(2{\left(\cos \left(45\right)\right)}^4-1+\frac{2}{2})\mathbf{÷}\frac{1}{2}}{\tau }}$$

Answered by Bagus1003 last updated on 09/Feb/22

$$\cos \left(45\right)=\frac{\sqrt{2}}{2}$$$${\left(\frac{\sqrt{2}}{2}\right)}^2=\frac{2}{4}=\frac{1}{2}$$$${\left(\frac{1}{2}\right)}^2=\frac{1}{4}$$$${\left(\frac{\sqrt{2}}{2}\right)}^4=\frac{1}{4}$$$$2\times \frac{1}{4}=\frac{1}{2}$$$$\frac{1}{2}=\frac{1}{2}\times \frac{\tau }{x\times 2}+1-\frac{2}{2}$$$$0.5=0.5\times \frac{\tau }{x\times 2}$$$$0.5/0.5=1$$$$Substitutethem$$$$1=\frac{\tau }{x\times 2}$$$$\tau =2\pi$$$$1=\frac{2\pi }{x\times 2}$$$$\left(x\times 2\right)1=\frac{2\pi }{x\times 2}\times \left(x\times 2\right)$$$$x\times 2=2\times \pi$$$$2/x\times 2=2\times \pi /2$$$$2/2=1$$$$Theresultofxis$$$$x=3.14..=\pi$$

Commented by MJS_new last updated on 09/Feb/22

$$\mathrm{LOL}!\mathrm{Thank}\mathrm{you}\mathrm{for}\mathrm{making}\mathrm{it}\mathrm{clear}!$$

Commented by Bagus1003 last updated on 09/Feb/22

$$Noproblemdude$$

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