Is ((cot(x)))/((csc(x)))=cos(x) ?

The answer to whether ((cot(x)))/((csc(x)))=cos(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove ((cot(x)))/((csc(x)))=cos(x)

prove

\frac{( cot ( x ) )}{( csc ( x ) )} = cos (x)

True

Solution steps

\frac{cot ( x )}{csc ( x )} = cos (x)

Manipulating left side

\frac{cot ( x )}{csc ( x )}

Express with sin, cos

\frac{cot ( x )}{csc ( x )}

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{\frac{c o s ( x )}{s i n ( x )}}{csc ( x )}

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{\frac{c o s ( x )}{s i n ( x )}}{\frac{1}{s i n ( x )}}

Simplify

\frac{\frac{c o s ( x )}{s i n ( x )}}{\frac{1}{s i n ( x )}} : cos (x)

\frac{\frac{c o s ( x )}{s i n ( x )}}{\frac{1}{s i n ( x )}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{cos ( x ) sin ( x )}{sin ( x ) \cdot 1}

Refine

= \frac{cos ( x ) sin ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

Is ((cot(x)))/((csc(x)))=cos(x) ?
The answer to whether ((cot(x)))/((csc(x)))=cos(x) is True