What is expand (1-cos(x))^3 ?

The solution to expand (1-cos(x))^3 is 1-3cos(x)+3cos^2(x)-cos^3(x)

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expand (1-cos(x))^3

expand

(1 - cos (x))^{3}

1 - 3 cos (x) + 3 cos^{2} (x) - cos^{3} (x)

Solution steps

(1 - cos (x))^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(1 - cos (x))^{3} = 1^{3} - 3 \cdot 1^{2} cos (x) + 3 \cdot 1 \cdot cos^{2} (x) - cos^{3} (x)

= 1^{3} - 3 \cdot 1^{2} cos (x) + 3 \cdot 1 \cdot cos^{2} (x) - cos^{3} (x)

Simplify

1^{3} - 3 \cdot 1^{2} cos (x) + 3 \cdot 1 \cdot cos^{2} (x) - cos^{3} (x) : 1 - 3 cos (x) + 3 cos^{2} (x) - cos^{3} (x)

= 1 - 3 cos (x) + 3 cos^{2} (x) - cos^{3} (x)

Ct an (π - x)

(a - b) (a + b)

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

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

(2 + x)^{2}

What is expand (1-cos(x))^3 ?
The solution to expand (1-cos(x))^3 is 1-3cos(x)+3cos^2(x)-cos^3(x)