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

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

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Answer 1 · 2017-11-30T09:28:16

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

Explanation:

I suppose you meant this,

$cos (4 θ) - 4 cos (2 θ) + 3$ $cos(4theta)-4cos(2theta)+3$

Let $2 θ$ $2theta$ be $x$ $x$ , and we get this,

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

Using double angle formulae,

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

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

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

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Explanation:

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