What is factor 1-2cos(2x)+cos^2(2x) ?

The solution to factor 1-2cos(2x)+cos^2(2x) is (cos(2x)-1)^2

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factor 1-2cos(2x)+cos^2(2x)

factor

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

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

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Rewrite

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

cos^{2} (2 x) - 2 cos (2 x) \cdot 1 + 1^{2}

= cos^{2} (2 x) - 2 cos (2 x) \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = cos (2 x), b = 1

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

(2) e^{2}

2 x (3 - 2 x)^{'} + 4 (x - 1)^{'}

[- 15.15]

\frac{x ^{2} + x - 2}{x - 1}

sin (3 x - 6 y)

What is factor 1-2cos(2x)+cos^2(2x) ?
The solution to factor 1-2cos(2x)+cos^2(2x) is (cos(2x)-1)^2