Is (cos(-x)tan(-x))/(sin(x))=-1 ?

The answer to whether (cos(-x)tan(-x))/(sin(x))=-1 is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove (cos(-x)tan(-x))/(sin(x))=-1

prove

\frac{cos ( - x ) tan ( - x )}{sin ( x )} = - 1

True

Solution steps

\frac{cos ( - x ) tan ( - x )}{sin ( x )} = - 1

Manipulating left side

\frac{cos ( - x ) tan ( - x )}{sin ( x )}

Use the negative angle identity:

cos (- x) = cos (x)

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

Use the negative angle identity:

tan (- x) = - tan (x)

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

Express with sin, cos

\frac{( - tan ( x ) ) cos ( x )}{sin ( x )}

Use the basic trigonometric identity:

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

= \frac{( - \frac{s i n ( x )}{c o s ( x )} ) cos ( x )}{sin ( x )}

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

\frac{( - \frac{s i n ( x )}{c o s ( x )} ) cos ( x )}{sin ( x )}

Remove parentheses:

(- a) = - a

= \frac{- \frac{s i n ( x )}{c o s ( x )} cos ( x )}{sin ( x )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{s i n ( x )}{c o s ( x )} cos ( x )}{sin ( x )}

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= sin (x)

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

Apply rule

\frac{a}{a} = 1

= - 1

= - 1

= - 1

We showed that the two sides could take the same form

\Rightarrow True

Is (cos(-x)tan(-x))/(sin(x))=-1 ?
The answer to whether (cos(-x)tan(-x))/(sin(x))=-1 is True