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}

ln (e^{5} - e^{3})

(2 x - 7)^{2} - 3 (2 x - 7) - 88

- 26 x^{6} + (- 2 z)

(x + 4) 2 + 5 (x + 4)

x^{2} 5 x - 6

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