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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cot (x)

Express with sin, cos

cot (x)

Use the basic trigonometric identity:

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

Divide fractions:

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

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

Refine

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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