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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand ((1-cos(x))^2+sin^2(x))/(1-cos(x))

expand

\frac{( 1 - cos ( x ) ) ^{2} + sin ^{2} ( x )}{1 - cos ( x )}

2

Solution steps

\frac{( 1 - cos ( x ) ) ^{2} + sin ^{2} ( x )}{1 - cos ( x )}

Expand

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

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

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

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

1 - 2 cos (x) + 1 = - 2 cos (x) + 2

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

Factor

- 2 cos (x) + 2 : 2 (- cos (x) + 1)

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

Cancel the common factor:

- cos (x) + 1

= 2

(x + \frac{1}{x})^{3}

(4 + 2) (6 - 2)

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

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

(x - 6)^{2}

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