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

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Answer 1 · 2017-11-30T09:28:16

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

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,

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

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