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}

1

2 (x + y)^{2} + 9 (x + y) - 5

(- 4.9) y^{8.5}

x^{2} - 5 x + 6.25

(a + b + c) (ab + a c + b c) - ab c

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