What is expand (1-cos(θ))^3 ?

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

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expand (1-cos(θ))^3

expand

(1 - cos (θ))^{3}

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

Solution steps

(1 - cos (θ))^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

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

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

\frac{x - 2}{( x - 1 ) ( x + 2 )}

(\frac{3 m}{4} + \frac{1}{6}) (\frac{m}{4} - \frac{5}{6})

(cos (4 x) + cos (3 x))^{2}

4 (1 - cos (θ))

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