Question

If `4cos^2(x)-3cos(x)=0` what is `cos(x)`?

Answer 1

`cos(x)=0color(white)("XX")orcolor(white)("XX")cos(x)=3/4`

Explanation:

It might be easier to think about this if you (temporarily) replace `cos(x)` with some variable, for example `k`

Then we have
`color(white)("XXX")4k^2-3k=0`

which can be factored as
`color(white)("XXX")k(4k-3)=0`

Which implies
`color(white)("XXX"){:(k=0,color(white)("XX")orcolor(white)("XX),4k-3=0),(,,rarrk=3/4):}`

But `k` is simply `cos(x)`

So
`color(white)("XXX"){:(cos(x)=0,color(white)("XX")orcolor(white)("XX"),cos(x)=3/4):}`