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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

sec (x) \cdot cot (x) = csc (x)

True

Solution steps

sec (x) cot (x) = csc (x)

Manipulating left side

sec (x) cot (x)

Express with sin, cos

cot (x) sec (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

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

Simplify

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= csc (x)

csc (x)

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ^{2} ( x )}{sec ( t )} = sec (t) - cos (t)

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

sec (A) csc (A) = tan (A) cot (A)

\frac{1 - cos ( 2 x )}{2} = 1 - cos^{2} (x)

tan^{4} (θ) - sec^{4} (θ) = 1 - 2 sec^{2} (θ)