What is expand (1-cos(x))^4 ?

The solution to expand (1-cos(x))^4 is 1-4cos(x)+6cos^2(x)-4cos^3(x)+cos^4(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1-cos(x))^4

expand

(1 - cos (x))^{4}

1 - 4 cos (x) + 6 cos^{2} (x) - 4 cos^{3} (x) + cos^{4} (x)

Solution steps

(1 - cos (x))^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = - cos (x)

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (- cos (x))^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- cos (x))^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- cos (x))^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- cos (x))^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- cos (x))^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- cos (x))^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (- cos (x))^{0} : 1

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (- cos (x))^{1} : - 4 cos (x)

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (- cos (x))^{2} : 6 cos^{2} (x)

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (- cos (x))^{3} : - 4 cos^{3} (x)

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (- cos (x))^{4} : cos^{4} (x)

= 1 - 4 cos (x) + 6 cos^{2} (x) - 4 cos^{3} (x) + cos^{4} (x)

\frac{10 x ^{2} y ^{2} - 8 x y ^{3} + 6 y}{2 y ^{2}}

\frac{1}{x ^{2} ( t x - 1 )}

sin^{2} (x) (cot (x) + 1)^{2}

\frac{1}{x ( x ^{2} + 5 )}

- (\frac{2 ( 2 s + 11 )}{( s ( s + 5 ) )})

What is expand (1-cos(x))^4 ?
The solution to expand (1-cos(x))^4 is 1-4cos(x)+6cos^2(x)-4cos^3(x)+cos^4(x)