Find solutions of the equation in the interval [0, 2pie}

Cos(x+pie/3)+Cos(x-pie/3)=1

I need to show work without calculator and be able to check in order for it to work

Thanks for help

3 answers

Cos(x+pie/3)+Cos(x-pie/3)=1
cosxcosπ/3 - sinxsinπ/3 + cosxcosπ/3 + sinxsinπ/2 = 1
2cosxcosπ/3 = 1
2cosx(1/2) = 1
cosx = 1
x = 0 or x = 2π

I will leave the checking up to you

thanks a lot

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