Is cos(x)csc(x)tan(x)=1 ?

The answer to whether cos(x)csc(x)tan(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)csc(x)tan(x)=1

prove

cos (x) csc (x) tan (x) = 1

True

Solution steps

cos (x) csc (x) tan (x) = 1

Manipulating left side

cos (x) csc (x) tan (x)

Express with sin, cos

cos (x) csc (x) tan (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

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

Cancel the common factor:

cos (x)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True