What is factor 4cos^2(x)-4cos(x)+1 ?

The solution to factor 4cos^2(x)-4cos(x)+1 is (2cos(x)-1)^2

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factor 4cos^2(x)-4cos(x)+1

factor

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

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

Solution steps

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

Rewrite

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

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

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

Apply Perfect Square Formula:

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

a = 2 cos (x), b = 1

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

x^{2} - a x + c x - a c

x^{6} + 3 x^{4} + 3 x^{2} + 1

- (cos (x) ln (sec (x) + tan (x)))

(a - b) + c

What is factor 4cos^2(x)-4cos(x)+1 ?
The solution to factor 4cos^2(x)-4cos(x)+1 is (2cos(x)-1)^2