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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Divide fractions:

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

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

Refine

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

Cancel the common factor:

sin (x)

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{1}{\frac{1}{s e c ( x )}}

Simplify

\frac{1}{\frac{1}{s e c ( x )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Apply rule

\frac{a}{1} = a

= sec (x)

sec (x)

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

9 sec^{2} (0) tan (0) = 12 tan (0)

cot (x) - sec (x) csc (x) cos (2 x) = tan (x)

tan (x) = \frac{3}{7} = cos (x)

3 - 6 sin^{2} (x) = 3 sin (2 x)

sin (2 z) = sin (z) cos (z) + cos (z) sin (z)

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