Question

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URGENT

Answer 1

2π/3&5π/3

Explanation:

2 cos(x)+1=0

i.e, cos(x) =(-1/2)

i.e, cos(x)= - cos (π/3)

i.e, cos(x)= cos(π-π/3) [since, cos(π-x) = -cosX]

i.e, cos(x)=cos2π/3

x=2π/3

or, cos(x)= -cos(π/3)

i.e, cos(x)=cos(π+π/3). [since, cos (π+x)= -cosx]

x=4π/3

✌️:)

Answer 2

`x=(2\pi )/(3),\:x=(4\pi )/(3)`

Explanation:

Alright so being presented with this equation the first thing we want to do is subtract 1 from both sides of
`2\cos \left(x\right)+1=0`.

`2\cos \left(x\right)+1-1=0-1`.

Now we want to simplify it to
`2\cos \left(x\right)=-1`.

Now go ahead and divide both sides by 2.
`(2\cos \left(x\right))/(2)=(-1)/(2)`

Make sure you simplify again to get
`\cos \left(x\right)=-(1)/(2)`.

Now you need your sin/cos periodicity table. When you look at the charts. Look for the general solutions of
`\cos \left(x\right)=-(1)/(2)`. After looking at the chart you will find
`x=(2\pi )/(3)+2\pi n,\:x=(4\pi )/(3)+2\pi n`.

Which we can then finalize at
`x=(2\pi )/(3),\:x=(4\pi )/(3)`.

Hope this helps!