Question

Simplify `cos(4theta)-4cos(2theta)+3`?

Answer 1

`2(cos(x)-1)^2`

Explanation:

I suppose you meant this,

`cos(4theta)-4cos(2theta)+3`

Let `2theta` be `x`, and we get this,

`cos(2x)-4cos(x)+3`

Using double angle formulae,

`cos(2x)-4cos(x)+3`
`=2cos^2(x)-1-4cos(x)+3`
`=2cos^2(x)-4cos(x)+2`
`=2(cos^2(x)-2cos(x)+1)`
`=2(cos(x)-1)^2`