Is 1/(sin(x)cos(x))=sec(x)csc(x) ?

The answer to whether 1/(sin(x)cos(x))=sec(x)csc(x) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove 1/(sin(x)cos(x))=sec(x)csc(x)

prove

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

True

Solution steps

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

Manipulating right side

sec (x) csc (x)

Express with sin, cos

csc (x) sec (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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