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Step-by-step Solution

Solve (1-cos(2*x))^2(1+cos(2*x))

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Answer

$-2\left(1-\cos\left(2x\right)\right)^2\sin\left(x\right)^2+2\left(1-\cos\left(2x\right)\right)^2$

Step-by-step explanation

Problem to solve:

$\left(1-\cos\left(2x\right)\right)^2\left(1+\cos\left(2x\right)\right)$
1

Applying an identity of double-angle cosine

$\left(1-\cos\left(2x\right)\right)^2\left(1+1-2\sin\left(x\right)^2\right)$
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Add the values $1$ and $1$

$\left(1-\cos\left(2x\right)\right)^2\left(-2\sin\left(x\right)^2+2\right)$

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Answer

$-2\left(1-\cos\left(2x\right)\right)^2\sin\left(x\right)^2+2\left(1-\cos\left(2x\right)\right)^2$
$\left(1-\cos\left(2x\right)\right)^2\left(1+\cos\left(2x\right)\right)$

Main topic:

Polynomials

Time to solve it:

~ 0.43 seconds

Related topics:


PolynomialsSpecial products