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

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

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

factor

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

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

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Rewrite

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

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

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

Apply Perfect Square Formula:

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

a = cos (x), b = 1

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

(- 3 m) + (- 4 n)

\frac{4 2 - 2}{3}

(x - y)^{2} - (x - y) - 2

(3 a + 5)^{2} - 18 (3 a + 5) + 81

x^{8} - 4

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