What is expand (1-cos^2(x))^2 ?

The solution to expand (1-cos^2(x))^2 is sin^4(x)

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expand (1-cos^2(x))^2

expand

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

sin^{4} (x)

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

1^{2} - 2 \cdot 1 \cdot cos^{2} (x) + (cos^{2} (x))^{2} : sin^{4} (x)

= sin^{4} (x)

\frac{x ( 2 x ^{2} - 5 )}{2 y ( y ^{2} - 2 )}

- \frac{2 ( 3 5 - 5 )}{5} + 1

\frac{1}{( x + 7 ) ^{2}}

\frac{e ^{- 5 s} ( 2 s + 3 )}{( s ^{2} + 2 s + 5 ) ( s )}

(4 y^{3} - 8 y^{2} - 3 x + 1) (y + \frac{1}{2})

What is expand (1-cos^2(x))^2 ?
The solution to expand (1-cos^2(x))^2 is sin^4(x)